Historically, the Roman Catholic Church has taught that infants who die before being baptized go to a portion of Hell that is without fire, also called Limbo:
Council of Florence (1445 AD)
Also, the souls of those who have incurred no stain of sin whatsoever after baptism, as well as souls who after incurring the stain of sin have been cleansed whether in their bodies or outside their bodies, as was stated above, are straightaway received into heaven and clearly behold the triune God as he is, yet one person more perfectly than another according to the difference of their merits. But the souls of those who depart this life in actual mortal sin, or in original sin alone, go down straightaway to hell to be punished, but with unequal pains.
With regard to children, since the danger of death is often present and the only remedy available to them is the sacrament of baptism by which they are snatched away from the dominion of the devil and adopted as children of God, it admonishes that sacred baptism is not to be deferred for forty or eighty days or any other period of time in accordance with the usage of some people, but it should be conferred as soon as it conveniently can; and if there is imminent danger of death, the child should be baptized straightaway without any delay, even by a lay man or a woman in the form of the church, if there is no priest, as is contained more fully in the decree on the Armenians.
Notice, the teaching of the ecumenical council is extremely clear. The fate of the unbaptized who die in "original sin alone" is unambiguously stated to be Hell. Any proposed exception to this would simply be a rejection of what the council says, when it provides absolutely no room for caveats. And, how could a caveat exist? Are any infants "more deserving" of an exception, than others?
Further, the council urges the immediate baptism of infants, because water baptism is "the only remedy available to them" to be kept from "the dominion of the devil".
The doctrine that infants go to Hell, but to a part of it that is without fire, is reiterated by Pope Pius VI (1717-1799 AD):
Pope Pius VI - Auctorem Fidei (1794 AD)
The Punishment of Those Who Die with Original Sin Only
26 The doctrine which rejects as a Pelagian fable, that place of the lower regions (which the faithful generally designate by the name of the limbo of children) in which the souls of those departing with the sole guilt of original sin are punished with the punishment of the condemned, exclusive of the punishment of fire, just as if, by this very fact, that these who remove the punishment of fire introduced that middle place and state free of guilt and of punishment between the kingdom of God and eternal damnation, such as that about which the Pelagians idly talk - false, rash, injurious to Catholic schools.
Above, what is being rejected as "false, rash, injurious to Catholic schools" is the doctrine that infants burn in Hell. Rather, he is affirming that they do in fact go to the "lower regions", i.e., Hell, to be "punished with the punishment of the condemned, exclusive of the punishment of fire", that is, without fire.
Also, Pope Sixtus V (1521-1590 AD) in the Papal Bull Effraenatam, which was to condemn abortion, says:
Pope Sixtus V - Effraenatam (1588 AD)
Noticing that frequently by various Apostolic Constitutions the audacity and daring of most profligate men, who know no restraint, of sinning with license against the commandment "do not kill" was repressed; We who are placed by the Lord in the supreme throne of justice, being counseled by a most just reason, are in part renewing old laws and in part extending them in order to restrain with just punishment the monstrous and atrocious brutality of those who have no fear to kill most cruelly fetuses still hiding in the maternal viscera.
Who will not detest such an abhorrent and evil act, by which are lost not only the bodies but also the souls? Who will not condemn to a most grave punishment the impiety of him who will exclude a soul created in the image of God and for which Our Lord Jesus Christ has shed His precious Blood, and which is capable of eternal happiness and is destined to be in the company of angels, from the blessed vision of God, and who has impeded as much as he could the filling up of heavenly mansions, and has taken away the service to God by His creature?
Above, the Pope clearly says that the "souls" of the infants are "lost", and the abortionist has "excluded a soul" from the "blessed vision of God", i.e., the Beatific Vision. This is the quintessence of Limbo - which in Catholic thought, does not necessarily confer pain, but does involve the deprivation of the Beatific Vision.
Finally, the Council of Trent (1545-1563 AD) stated clearly that baptism is required for remission of "original sin", and entrance into Heaven, both generally, and specifically when speaking in the context of unbaptized infants:
Council of Trent (1547 AD) - Session 7
2 If any one shall say, that true and natural water is not of necessity for baptism, and, on that account, wrests to some sort of metaphor those words of our Lord Jesus Christ; Except a man be born again of water and them Holy Ghost; let him be anathema.
5 If any one shall say, that baptism is free, that is, not necessary unto salvation; let him be anathema.
Council of Trent (1546 AD) - Session 5
4 If any one denies that infants, newly born from their mothers' wombs, even though they be sprung from baptized parents, are to be baptized; or says that they are baptized indeed for the remission of sins, but that they draw nought of original sin from Adam, which has need to be expiated by the laver of regeneration, for the obtaining life everlasting - whence it follows, as a consequence, that in them the form of baptism, for the remission of sins, is understood to be not true, but false - let him be anathema. For that which the apostle has said, By one man sin entered into the world, and by sin death, and so death passed upon all men in whom all have sinned, is not to be understood otherwise than as the Catholic Church spread everywhere hath always understood it. For, by reason of this rule of faith, from a tradition of the apostles, even infants, who could not as yet in themselves commit any sin, are for this cause truly baptized for the remission of sins, that in them that which they have contracted by generation, may be cleansed away by regeneration. For, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God.
Above, in yet another ecumenical council, the Church is mandating infant baptism on the basis that it is necessary for Salvation.
And, it is again worth stating that no exceptions are provided for in the text, neither would any exceptions be logically possible. In what case would there be an exception? When the baby's parents aren't Christian? Is a Christian baby any more to blame than a non-Christian baby, for not being baptized? Either way, the child is admittedly innocent, having "original sin" only. So, no exception is given, because the doctrine leaves no room for exceptions.
In October of 2004, Pope John Paul II (1920-2005 AD) tasked the Church's International Theological Commission with studying the question of the possibility for salvation of unbaptized infants. This study was completed under the pontificate of Pope Benedict XVI (1927-2022 AD), and the Pope approved the document submitted by the commission on January 19, 2007.
This document stated:
The Hope of Salvation for Infants Who Die Without Being Baptized (2007 AD)
102 Our conclusion is that the many factors that we have considered above give serious theological and liturgical grounds for hope that unbaptized infants who die will be saved and enjoy the Beatific Vision. We emphasize that these are reasons for prayerful hope, rather than grounds for sure knowledge.
The above conclusion, promulgated by Pope Benedict XVI, is directly contradictory to the explicit statements covered in the first section of this article, particularly those of the Council of Florence.
Recall that the Council of Florence stated that water baptism is "the only remedy available" to infants to be kept from "the dominion of the devil", and that all who die "in original sin alone, go down straightaway to hell". That's perfectly, unambiguously clear. As were Pope Pius VI, Pope Sixtus V, and the Council of Trent.
Their failure to dogmatically take a stand for the Church's historical doctrine of Limbo presents a contradiction, even if Limbo is not explicitly denied. It is the same as if someone said "The sky is blue", repeatedly, for many years, then when challenged, sheepishly said "There is reason to hope that the sky is not blue". It is a different message.
The modern Catechism of the Catholic Church also states a hope for the Salvation unbaptized infants, again contravening historical Roman Catholicism:
Catechism of the Catholic Church 1261
1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them," allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.
The above, along with the document promulgated by Pope Benedict XVI, is the simple result of kind people who are rightfully appalled at the Church's historical false doctrine, and so resort to dishonestly pretending that the Church's clear statements on the matter can be ignored, or nullified. They are trying to square a theological circle, which requires them to start playing with language, and other deceptive, dishonest tactics. The Church was not silent on this issue, it was unambiguous, and slammed the door on the "hope" that the modern Catholic Church professes, many hundreds of years ago.
In the past, the Church clearly and repeatedly taught that infants who die without water baptism go to a section of Hell known as Limbo. It was a well-established, authentic tradition of the Church, taught and believed by the "Vicar of Christ". However, in modern times, the Church has denied that the fate of unbaptized infants is necessarily Limbo, but rather hopes that they too may go to Heaven.
The Church's failure to dogmatically stand behind Limbo, even though Limbo was taught by an ecumenical council and multiple Popes, presents another modern contradiction of convenience for the Roman Catholic Church. These are such that come about by the Church wanting to distance itself from doctrines that it definitely held and taught in the past, because such doctrines are horrific to modern sensibilities. See, for instance, the death penalty, criminalizing homosexuality, banning female altar servers, torturing heretics, confining Jews to ghettos, etc.