Historically, the Catholic Church has taught explicitly that unless one is a Roman Catholic, they will go to Hell. This is known as Extra Ecclesiam Nulla Salus - "Outside of the Church, there is no Salvation".
For instance, in Pope Boniface VIII's (1230-1303 AD) Ex Cathedra Papal Bull Unam Sanctam, we read:
Pope Boniface VIII - Unam Sanctam (1302 AD)
Urged by faith, we are obliged to believe and to maintain that the Church is one, holy, catholic, and also apostolic. We believe in her firmly and we confess with simplicity that outside of her there is neither salvation nor the remission of sins
Therefore, if the Greeks or others should say that they are not confided to Peter and to his successors, they must confess not being the sheep of Christ, since Our Lord says in John "there is one sheepfold and one shepherd."
Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.
Notice that "subjection to the Roman Pontiff" is explicity defined as a requirement for Salvation. And, non-Catholics, namely the Greek Orthodox, "or others" who are not under the Pope, the Church confesses as "not being the sheep of Christ". Also, the fact that this condemns all non-Catholics is manifest by his use of of the term "every human creature" - which clearly is intended to encompass all people, regardless of their profession of faith.
Another clear testament to there being no Salvation outside the Roman Catholic Church is the Ex Cathedra Papal Bull Cantate Domino, issued by Pope Eugene IV (1383-1447 AD), which was incorporated into the Council of Florence (1445 AD):
Pope Eugene IV - Cantate Domino (1442 AD)
It firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart "into everlasting fire which was prepared for the devil and his angels" (Matt. 25:41), unless before the end of life the same have been added to the flock; and that the unity of the ecclesiastical body is so strong that only to those remaining in it are the sacraments of the Church of benefit for salvation, and do fastings, almsgiving, and other functions of piety and exercises of Christian service produce eternal reward, and that no one, whatever almsgiving he has practiced, even if he has shed blood for the name of Christ, can be saved, unless he has remained in the bosom and unity of the Catholic Church.
Above, "heretics", which are Christians who believe false doctrines, are explicitly called out as those who are to be damned - "even if he has shed blood for the name of Christ". Pagans and Jews are also explicitly named as those who are to be damned.
There are many such statements in Papal Bulls and Encyclicals through the centuries, which specifically indicate the need for subjection to the Roman Catholic Church, and its doctrines, in order to be saved:
Pope Clement VI - Super Quibusdam (1351 AD)
In the second place, we ask whether you and the Armenians obedient to you believe that no man of the wayfarers outside the faith of this Church, and outside the obedience to the Pope of Rome, can finally be saved.
Pope Pius VI - Charitas (1791 AD)
Finally, in one word, stay close to Us. For no one can be in the Church of Christ without being in unity with its visible head and founded on the See of Peter.
Pope Leo XIII - Satis Cognitum (1896 AD)
9 The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium. Epiphanius, Augustine, Theodoret, drew up a long list of the heresies of their times. St. Augustine notes that other heresies may spring up, to a single one of which, should any one give his assent, he is by the very fact cut off from Catholic unity. "No one who merely disbelieves in all (these heresies) can for that reason regard himself as a Catholic or call himself one. For there may be or may arise some other heresies, which are not set out in this work of ours, and, if any one holds to one single one of these he is not a Catholic".
Pope Benedict XV - Ad Beatissimi Apostolorum (1914 AD)
24 Such is the nature of Catholicism that it does not admit of more or less, but must be held as a whole or as a whole rejected: "This is the Catholic faith, which unless a man believe faithfully and firmly; he cannot be saved" (Athanasian Creed).
Pope Pius XI - Mortalium Animos (1928 AD)
11 Furthermore, in this one Church of Christ no man can be or remain who does not accept, recognize and obey the authority and supremacy of Peter and his legitimate successors. Did not the ancestors of those who are now entangled in the errors of Photius and the reformers, obey the Bishop of Rome, the chief shepherd of souls? ... Let them hear Lactantius crying out: "The Catholic Church is alone in keeping the true worship. This is the fount of truth, this the house of Faith, this the temple of God: if any man enter not here, or if any man go forth from it, he is a stranger to the hope of life and salvation. Let none delude himself with obstinate wrangling. For life and salvation are here concerned, which will be lost and entirely destroyed, unless their interests are carefully and assiduously kept in mind."
For conciliar support, we can turn to the decrees issued during the Council of Trent (1545-1563 AD), the great Counter-Reformation council.
The Council of Trent pronounces Anathemas on scores of offenses and heresies - over 130. For the Catholic definition of "Anathema", we can consult the Catholic Encyclopedia, which quotes the formal Anathema pronouncement:
Anathema Pronouncement - Catholic Encyclopedia: "Anathema"
Wherefore in the name of God the All-powerful, Father, Son, and Holy Ghost, of the Blessed Peter, Prince of the Apostles, and of all the saints, in virtue of the power which has been given us of binding and loosing in Heaven and on earth, we deprive (name) himself and all his accomplices and all his abettors of the Communion of the Body and Blood of Our Lord, we separate him from the society of all Christians, we exclude him from the bosom of our Holy Mother the Church in Heaven and on earth, we declare him excommunicated and anathematized and we judge him condemned to eternal fire with Satan and his angels and all the reprobate, so long as he will not burst the fetters of the demon, do penance and satisfy the Church; we deliver him to Satan to mortify his body, that his soul may be saved on the day of judgment.
The above clearly indicates that if someone is under an Anathema, they are bound to Hell until they repent. Pronouncing an Anathema on someone is authoritatively consigning them to Hell, as you are declaring them to be outside of the Church - "outside of which there is absolutely no Salvation" (Fourth Lateran Council, 1215 AD).
This is bolstered by the explicit definition of "Anathema" given at the Second Council of Nicaea (787 AD):
Second Council of Nicaea (787 AD)
Now anathema is nothing less than complete separation from God. For if any are quarrelsome and will not obediently accept what has now been decreed, they but kick against the pricks, and injure their own souls in their fighting against Christ.
Above, we again see that Anathema unambiguously consigns one to damnation - "complete separation from God" - which is how Scripture describes Hell (2 Thessalonians 1:8-9).
Some of the Anathematized beliefs, according to the Council of Trent are as follows:
This small sampling is sufficient to demonstrate that if a person disagrees with what the Catholic Church teaches on dozens of topics, they are anathematized from the Church, which consigns them to Hell. This council was specifically targeted at repudiating the beliefs of Protestants, and Protestantism.
Eastern Orthodoxy, too, was specifically repudiated as heretical by the Ecumenical Councils of Lyons and Florence, in which the Filioque clause ("and the Son") in the Nicence Creed - something rejected by all Eastern Orthodox - was solemnly affirmed, and dissenters to it were anathematized:
Second Council of Lyons (1274 AD) - Constitution 2
1 We profess faithfully and devotedly that the holy Spirit proceeds eternally from the Father and the Son, not as from two principles, but as from one principle; not by two spirations, but by one single spiration. This the holy Roman church, mother and mistress of all the faithful, has till now professed, preached and taught; this she firmly holds, preaches, professes and teaches; this is the unchangeable and true belief of the orthodox fathers and doctors, Latin and Greek alike. But because some, on account of ignorance of the said indisputable truth, have fallen into various errors, we, wishing to close the way to such errors, with the approval of the sacred council, condemn and reprove all who presume to deny that the holy Spirit proceeds eternally from the Father and the Son, or rashly to assert that the holy Spirit proceeds from the Father and the Son as from two principles and not as from one.
Council of Florence (1442 AD) - Session 11
The holy Spirit is from the Father and the Son; not made nor created nor begotten, but proceeding. So there is one Father, not three fathers; one Son, not three sons; one holy Spirit, not three holy spirits. And in this Trinity nothing is before or after, nothing is greater or less; but the whole three persons are co-eternal together and co-equal. So that in all things, as has been said above, the unity in Trinity and the Trinity in unity is to be worshipped. Whoever, therefore, wishes to be saved, let him think thus of the Trinity.
The existence of the Son from the Father is certainly eternal and without beginning, and the procession of the holy Spirit from the Father and the Son is eternal and without beginning.
Therefore it condemns, reproves, anathematizes and declares to be outside the body of Christ, which is the church, whoever holds opposing or contrary views.
Therefore, all Protestants and Orthodox - not to mention Jews and Pagans - have been explicitly condemned as heretics, alien from the Catholic Church, in many different infallible documents promulgated by the Church.
For more than a dozen additional references for this teaching, see Appendix I at the end of this article.
The first prominent indication of an authoritative change in teaching on this issue can be seen in an Encyclical of Pope Pius IX (1792-1878 AD), entitled Quanto Conficiamur Moerore:
Pope Pius IX - Quanto Conficiamur Moerore (1863 AD)
7 Here, too, our beloved sons and venerable brothers, it is again necessary to mention and censure a very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion. Sincerely observing the natural law and its precepts inscribed by God on all hearts and ready to obey God, they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace. Because God knows, searches and clearly understands the minds, hearts, thoughts, and nature of all, his supreme kindness and clemency do not permit anyone at all who is not guilty of deliberate sin to suffer eternal punishments.
8 Also well known is the Catholic teaching that no one can be saved outside the Catholic Church. Eternal salvation cannot be obtained by those who oppose the authority and statements of the same Church and are stubbornly separated from the unity of the Church and also from the successor of Peter, the Roman Pontiff, to whom “the custody of the vineyard has been committed by the Savior.”
Here, we see two important details:
It should be noted that the traditionalist view of the concept of invincible ignorance as taught by Pope Pius IX is that invincible ignorance doesn't save a person. It simply means that you don't incur the specific sin for rejecting a truth that you haven't been exposed to. In other words, you still don't have the new birth, conferred by baptism, and are lost, but aren't condemned specifically for rejecting all of the teachings that you are ignorant of.
Regardless, the concept of invincible ignorance would provide the basis for a wholesale overthrow of Catholic teaching regarding Extra Ecclesiam Nulla Salus.
This complete overthrow took place during the Second Vatican Council (1962-1965 AD). In one of the declarations entitled Lumen Gentium, they begin by affirming Pius IX's position in Quanto Conficiamur Moerore:
Vatican 2 (1965 AD) - Lumen Gentium
14 This Sacred Council wishes to turn its attention firstly to the Catholic faithful. Basing itself upon Sacred Scripture and Tradition, it teaches that the Church, now sojourning on earth as an exile, is necessary for salvation. Christ, present to us in His Body, which is the Church, is the one Mediator and the unique way of salvation. In explicit terms He Himself affirmed the necessity of faith and baptism and thereby affirmed also the necessity of the Church, for through baptism as through a door men enter the Church. Whosoever, therefore, knowing that the Catholic Church was made necessary by Christ, would refuse to enter or to remain in it, could not be saved.
Notice the caveat of invincible ignorance - only those "knowing that the Catholic Church was made necessary by Christ, would refuse to enter or to remain in it", are going to be damned. All others may be saved in the Church, unbeknownst to them, in invincible ignorance.
This invincibly ignorant group is addressed in various of the declarations of Vatican 2:
Nostra Aetate mentions by name Hindus, Buddhists, Muslims, and Jews, using language designed to foster ecumenism and dialogue. However, in the case of Islam specifically, the language used crosses the line into flagrant heresy:
Vatican 2 (1965 AD) - Nostra Aetate
3 The Church regards with esteem also the Moslems. They adore the one God, living and subsisting in Himself; merciful and all-powerful, the Creator of heaven and earth, who has spoken to men; they take pains to submit wholeheartedly to even His inscrutable decrees, just as Abraham, with whom the faith of Islam takes pleasure in linking itself, submitted to God. Though they do not acknowledge Jesus as God, they revere Him as a prophet. They also honor Mary, His virgin Mother; at times they even call on her with devotion. In addition, they await the day of judgment when God will render their deserts to all those who have been raised up from the dead. Finally, they value the moral life and worship God especially through prayer, almsgiving and fasting.
The above states that "They adore the one God", and "worship God, especially through prayer, almsgiving, and fasting". The issue, Biblically, is that they do no such thing. They worship an idol (1 Chronicles 16:26), who is a demon (1 Corinthians 10:20). Extolling Allah as "merciful and all-powerful" is merely referring to their suppositions, which are actually self-deception and lies. This only serves to appeal to their delusion, and perpetuate their error.
The Gentiles were, without question, sincere in their worship of false gods. Yet, what does the Apostle Paul call them?:
1 Corinthians 10:20
20 But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils.
Muslims do not worship God, because they reject that God has any son (Surah 19:88-92), and if anyone does not have the Son of God, they do not have God (1 John 2:23: 2 John 1:9, etc.).
This error is reiterated in Lumen Gentium:
Vatican 2 (1965 AD) - Lumen Gentium
16 But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Muslims, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things, and as Saviour wills that all men be saved. Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience.
Notice that now the plan of Salvation includes "those who acknowledge the Creator", which could refer to any religious system on the face of the earth. And, it says that Muslims "along with us, adore the one and merciful God". This is erroneous and heretical for the same reasons discussed above.
The fact that the caveat of invincible ignorance is applied to virtually all religions is clarified repeatedly in the Catechism (Catechism of the Catholic Church 841, 847, 1260, 1281). So long as they are sufficiently ignorant, they can be saved, regardless of what religion they follow.
Finally, coming to Vatican 2's Unitatis Redintegratio, this offer of Salvation is extended even to Protestants - a group that is literally defined by its rejection of Roman Catholic doctrines:
Vatican 2 (1965 AD) - Unitatis Redintegratio
3 For men who believe in Christ and have been truly baptized are in communion with the Catholic Church even though this communion is imperfect. The differences that exist in varying degrees between them and the Catholic Church - whether in doctrine and sometimes in discipline, or concerning the structure of the Church - do indeed create many obstacles, sometimes serious ones, to full ecclesiastical communion. The ecumenical movement is striving to overcome these obstacles. But even in spite of them it remains true that all who have been justified by faith in Baptism are members of Christ's body, and have a right to be called Christian, and so are correctly accepted as brothers by the children of the Catholic Church.
The brethren divided from us also use many liturgical actions of the Christian religion. These most certainly can truly engender a life of grace in ways that vary according to the condition of each Church or Community. These liturgical actions must be regarded as capable of giving access to the community of salvation.
It follows that the separated Churches and Communities as such, though we believe them to be deficient in some respects, have been by no means deprived of significance and importance in the mystery of salvation. For the Spirit of Christ has not refrained from using them as means of salvation which derive their efficacy from the very fullness of grace and truth entrusted to the Church.
Every single Protestant denomination holds to one or more anathematized beliefs in the Council of Trent, or other preceding councils. The same is true of every Eastern Orthodox Christian. Therefore, the above affirmation necessarily contradicts prior infallible declarations, if such can be saved.
The idea that heretical Christian groups - which all non-Catholics are considered, by the Roman Catholic Church - can be saved, is a contradiction of Church history. I encourage you to re-read the declarations given in the first section of this article, and those in Appendix I, to fully grasp the absurdity of these statements from Vatican 2, and the modern Catechism.
Somehow, we are to believe that "it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff" (Unam Sanctam), and yet a member of virtually any religion or Christian denomination whatsoever, can be saved. This is the cognitive dissonance demanded, in order to accept a clear contradiction, and revision of doctrine.
Can any honest person read all the historical pronouncements of the Popes and Councils, and conclude that they all had invincible ignorance in mind, when making those declarations? Does anyone believe that, if they were to ask the bishops at the Fourth Lateran Council (1215 AD), who said "There is one Universal Church of the faithful, outside of which there is absolutely no salvation", if they actually meant to include all of those included by Vatican 2, that they would say yes?
Of course not. They never mentioned this caveat of invincible ignorance, for a reason. Invincible ignorance is a late invention, which is then foisted retroactively on statements which, in context, totally disallow it, and taken in historical context, demonstrate their opposition to it - the Roman Catholic Church persecuted and killed the same groups mentioned in Vatican 2, repeatedly, over the centuries in which those exclusivist declarations were being made. Were they persecuting and killing "separated brethren", or unwitting members of their own Church? What would they have said, had you asked them? They would have said absolutely not.
And, they have not only twisted their own predecessors' words, but also the Word of God, which says:
John 3:36
36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
If someone were to come along later, and assert that John the Baptist was actually saying "You will also have Everlasting Life if you believe in Buddha, but it will be through Jesus", every single person would recognize that for what it is - twisting words, and introducing something into another person's statement that they had no concept of, and would have rejected wholesale had you asked them. This is a way to make words meaningless, by nullifying what was clearly the original intent.
For most of its history, the Roman Catholic Church taught that all non-Roman Catholics would be damned, with absolutely no caveats ever mentioned or provided for. In modern times, they have contradicted this doctrine, with the introduction of invincible ignorance, which in Vatican 2, was extended to encompass groups which previous Popes and Councils explicitly anathematized.
The concept of invincible ignorance is rooted in a fundamental misunderstanding of how a person is justified before God. We are justified in the sight of God by the imputed righteousness of Christ, when we believe in Him (Romans 3:21-22, 4:4-8). Outside of that, there is no Salvation, because none can be justified by living a righteous life (Romans 3:20). For this reason, the Bible is clear in teaching that all non-believers will go to Hell (John 3:18, 3:36, 8:24, 14:6, Mark 16:16, Acts 4:12: 1 John 5:12). The situation of those who never hear about the Gospel is discussed in this article.
Extra Ecclesiam Nulla Salus is true, however, the Church is not an ecclesiastical institution like the Roman Catholic Church. Rather, it is the body of Christ (Ephesians 1:22-23, Colossians 1:18, 1:24), which consists of every believer in Jesus. The historical Catholic Church misdefined the Church as the Roman Catholic Church, and the modern Catholic Church rejects the entire Biblical doctrine, except in a token, meaningless way, which removes any meaningful definition of the Church.
Pope Gregory the Great - quoted in Summo Iugiter Studio (590-604 AD)
The holy universal Church teaches that it is not possible to worship God truly except in her and asserts that all who are outside of her will not be saved.
Pope Innocent III - Eius Exemplo (1208 AD)
By the heart we believe and by the mouth we confess the one Church, not of heretics, but the Holy Roman, Catholic, and Apostolic Church outside of which we believe that no one is saved.
Fourth Lateran Council (1215 AD)
1 There is one Universal Church of the faithful, outside of which there is absolutely no salvation.
Pope Pius IV - The Tridentine Creed (1563 AD)
I condemn, reject, and anathematize all things contrary thereto, and all heresies which the Church hath condemned, rejected, and anathematized. This true Catholic faith, outside of which no one can be saved, which I now freely profess and to which I truly adhere, inviolate and with firm constancy until the last breath of life, I do so profess and swear to maintain with the help of God.
Pope Pius V - Regnans in Excelsis (1570 AD)
The sovereign jurisdiction of the one holy Catholic and Apostolic Church, outside of which there is no salvation, has been given by Him [Jesus Christ], unto Whom all power in Heaven and on Earth is given, the King who reigns on high, but to one person on the face of the Earth, to Peter, prince of the Apostles... If any shall contravene this Our decree, we bind them with the same bond of anathema.
Pope Leo XII - Ubi Primum (1824 AD)
It is impossible for the most true God, who is Truth itself, the best, the wisest Provider, and the Rewarder of good men, to approve all sects who profess false teachings which are often inconsistent with one another and contradictory, and to confer eternal rewards on their members… by divine faith we hold one Lord, one faith, one baptism… This is why we profess that there is no salvation outside the Church.
Pope Leo XII - Quod Hoc Ineunte (1824 AD)
We address all of you who are still removed from the true Church and the road to salvation. In this universal rejoicing, one thing is lacking: that having been called by the inspiration of the Heavenly Spirit and having broken every decisive snare, you might sincerely agree with the mother Church, outside of whose teachings there is no salvation.
Pope Gregory XVI - Summo Iugiter Studio (1832 AD)
Finally some of these misguided people attempt to persuade themselves and others that men are not saved only in the Catholic religion, but that even heretics may attain eternal life.
Pope Gregory XVI - Mirari Vos (1832 AD)
With the admonition of the apostle, that ‘there is one God, one faith, one baptism’ (Eph. 4:5), may those fear who contrive the notion that the safe harbor of salvation is open to persons of any religion whatever. They should consider the testimony of Christ Himself that 'those who are not with Christ are against Him,' (Lk. 11:23) and that they disperse unhappily who do not gather with Him. Therefore, 'without a doubt, they will perish forever, unless they hold the Catholic faith whole and inviolate (Athanasian Creed).
Pope Pius IX - Ubi Primum (1847 AD)
For there is one universal Church outside of which no one at all is saved; it contains regular and secular prelates along with those under their jurisdiction, who all profess one Lord, one faith and one baptism.
Pope Pius IX - Nostis et Nobiscum (1849 AD)
In particular, ensure that the faithful are deeply and thoroughly convinced of the truth of the doctrine that the Catholic faith is necessary for attaining salvation. (This doctrine, received from Christ and emphasized by the Fathers and Councils, is also contained in the formulae of the profession of faith used by Latin, Greek and Oriental Catholics).
Pope Pius IX - Amantissimus (1862 AD)
3 There are other, almost countless, proofs drawn from the most trustworthy witnesses which clearly and openly testify with great faith, exactitude, respect and obedience that all who want to belong to the true and only Church of Christ must honor and obey this Apostolic See and Roman Pontiff.
Pope Pius IX - Quanta Cura (1864 AD), Syllabus of Errors
16 "Man may, in the observance of any religion whatever, find the way of eternal salvation, and arrive at eternal salvation." (Condemned)
Vatican 1 (1870 AD) - Session 2
Likewise all other things which have been transmitted, defined and declared by the sacred canons and the ecumenical councils, especially the sacred Trent, I accept unhesitatingly and profess; in the same way whatever is to the contrary, and whatever heresies have been condemned, rejected and anathematised by the church, I too condemn, reject and anathematise.
This true catholic faith, outside of which none can be saved, which I now freely profess and truly hold, is what I shall steadfastly maintain and confess, by the help of God, in all its completeness and purity until my dying breath, and I shall do my best to ensure that all others do the same.
Vatican 1 (1870 AD) - Session 4
Therefore, if anyone says that it is not by the institution of Christ the lord himself (that is to say, by divine law) that blessed Peter should have perpetual successors in the primacy over the whole church; or that the Roman pontiff is not the successor of blessed Peter in this primacy: let him be anathema.
So, then, if anyone says that the Roman pontiff has merely an office of supervision and guidance, and not the full and supreme power of jurisdiction over the whole church, and this not only in matters of faith and morals, but also in those which concern the discipline and government of the church dispersed throughout the whole world; or that he has only the principal part, but not the absolute fullness, of this supreme power; or that this power of his is not ordinary and immediate both over all and each of the churches and over all and each of the pastors and faithful: let him be anathema.
Pope Leo XIII - Sapientiae Christianae (1890 AD)
22 Now, as the Apostle Paul urges, this unanimity ought to be perfect. Christian faith reposes not on human but on divine authority, for what God has revealed "we believe not on account of the intrinsic evidence of the truth perceived by the natural light of our reason, but on account of the authority of God revealing, who cannot be deceived nor Himself deceive." It follows as a consequence that whatever things are manifestly revealed by God we must receive with a similar and equal assent. To refuse to believe any one of them is equivalent to rejecting them all, for those at once destroy the very groundwork of faith who deny that God has spoken to men, or who bring into doubt His infinite truth and wisdom.
Pope Leo XIII - Satis Cognitum (1896 AD)
13 And for a like reason St. Augustine publicly attests that, "the primacy of the Apostolic chair always existed in the Roman Church" (Ep. xliii., n. 7); and he denies that anyone who dissents from the Roman faith can be a Catholic. "You are not to be looked upon as holding the true Catholic faith if you do not teach that the faith of Rome is to be held" (Sermo cxx., n. 13). So, too, St. Cyprian: "To be in communion with Cornelius is to be in communion with the Catholic Church" (Ep. lv., n. 1). In the same way Maximus the Abbot teaches that obedience to the Roman Pontiff is the proof of the true faith and of legitimate communion. Therefore if a man does not want to be, or to be called, a heretic, let him not strive to please this or that man...but let him hasten before all things to be in communion with the Roman See. If he be in communion with it, he should be acknowledged by all and everywhere as faithful and orthodox. He speaks in vain who tries to persuade me of the orthodoxy of those who, like himself, refuse obedience to his Holiness the Pope of the most holy Church of Rome: that is to the Apostolic See."
Pope Leo XIII - Tametsi Futura Prospicientibus (1900 AD)
Christ is man's 'Way'; the Church also is his 'Way'... Hence all who would find salvation apart from the Church, are led astray and strive in vain.
Pope Pius X - Iucunda Sane (1904 AD)
9 Yet at the same time We cannot but remind all, great and small, as Pope St. Gregory did, of the absolute necessity of having recourse to this Church in order to have eternal salvation, to follow the right road of reason, to feed on the truth, to obtain peace and even happiness in this life.
Pope Pius X - Acerbo Nimis (1905 AD)
2 And so Our Predecessor, Benedict XIV, had just cause to write: "We declare that a great number of those who are condemned to eternal punishment suffer that everlasting calamity because of ignorance of those mysteries of faith which must be known and believed in order to be numbered among the elect."
Pope Pius XII - Mystici Corporis Christi (1943 AD)
22 Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed.
41 They, therefore, walk in the path of dangerous error who believe that they can accept Christ as the Head of the Church, while not adhering loyally to His Vicar on earth. They have taken away the visible head, broken the visible bonds of unity and left the Mystical Body of the Redeemer so obscured and so maimed, that those who are seeking the haven of eternal salvation can neither see it nor find it.
Pope Pius XII - Humani Generis (1950 AD)
27 Some say they are not bound by the doctrine, explained in Our Encyclical Letter of a few years ago, and based on the Sources of Revelation, which teaches that the Mystical Body of Christ and the Roman Catholic Church are one and the same thing. Some reduce to a meaningless formula the necessity of belonging to the true Church in order to gain eternal salvation. Others finally belittle the reasonable character of the credibility of Christian faith.