In the Quran, there is a relatively clear statement made by Muhammad in Surah 2 regarding the fate of Christians:
Surah 2:62
62 Indeed, the believers, Jews, Christians, and Sabians - whoever believes in Allah and the Last Day and does good will have their reward with their Lord. And there will be no fear for them, nor will they grieve.
Since elsewhere in the Quran, Muhammad acknowledges that Allah is the God worshipped by Christians and Jews (Surah 5:43-47), above is saying that so long as someone believes in God, believes in judgement day, and does good works, they will be fine, even if they are Christians or Jews. They have nothing to fear, in fact, they will be rewarded.
This statement is repeated almost verbatim in Surah 5:
Surah 5:68-69
68 Say, ˹O Prophet,˺ “O People of the Book! You have nothing to stand on unless you observe the Torah, the Gospel, and what has been revealed to you from your Lord.” And your Lord’s revelation to you ˹O Prophet˺ will only cause many of them to increase in wickedness and disbelief. So do not grieve for the people who disbelieve.
69 Indeed, the believers, Jews, Sabians and Christians - whoever believes in Allah and the Last Day and does good, there will be no fear for them, nor will they grieve.
In spite of the above, just three verses later in Surah 5:72, Muhammad says all who believe that Jesus is God will go to Hell, just as he had done earlier in the same chapter (Surah 5:17). Muhammad nothing about "Christianity" at all, so felt comfortable affirming Christians, and their Scripture, despite explicitly condemning all but a tiny, heretical subset to Hell just a few verses later.
In addition to the two explicitly inclusive, ecumenical statements above, later in Surah 2, Muhammad actually condemns the Jews and Christians for their exclusivist beliefs:
Surah 2:94, 111-112
94 Say, ˹O Prophet,˺ “If the ˹eternal˺ Home of the Hereafter with Allah is exclusively for you ˹Israelites˺ out of all humanity, then wish for death if what you say is true!”
111 The Jews and Christians each claim that none will enter Paradise except those of their own faith. These are their desires. Reply, ˹O Prophet,˺ “Show ˹me˺ your proof if what you say is true.”
112 But no! Whoever submits themselves to Allah and does good will have their reward with their Lord. And there will be no fear for them, nor will they grieve.
This is yet another statement to the effect that any generally "good" person who believes in God is accepted by Him, and is also an explicit condemnation of exclusivism.
The message is already getting muddy. Christians and Jews are acceptable to God, so long as they don't believe anything any Christian has ever believed, and one of the errors of the Jews and the Christians is their exclusivism, even though all those Christians are going to Hell. Luckily, we can continue reading the Quran to make it abundantly clear that despite the lip service above, it teaches that all non-Muslims are going straight to Hell.
Surah 3 contains statements that directly contradicts the teaching that any "Jews, Christians, or Sabians" could ever be accepted by God:
Surah 3:19, 85
19 Certainly, Allah’s only Way is Islam. Those who were given the Scripture did not dispute ˹among themselves˺ out of mutual envy until knowledge came to them. Whoever denies Allah’s signs, then surely Allah is swift in reckoning.
85 Whoever seeks a way other than Islam, it will never be accepted from them, and in the Hereafter they will be among the losers.
Clearly, these verses teach that only Islam is acceptable to God, which totally contradicts Surah 2:62 and 5:69. If you aren't a Muslim, you will be condemned in the hereafter, meaning "Jews, Christians, and Sabians" will fear on Judgement Day, and will grieve, making Surah 2:62, 5:69 false, and meaningless.
Another passage in Surah 98 also makes it clear that those who reject the truth of Islam will burn in Hell, and are the worst of creatures:
Surah 98:6
6 Indeed, those who disbelieve from the People of the Book and the polytheists will be in the Fire of Hell, to stay there forever. They are the worst of ˹all˺ beings.
In the Quran, the "People of the Book" refers to Jews and Christians.
So, from the Quran, we learn that "Christians, Jews, and Sabians" have nothing to fear on Judgment Day, and teach the baseless lie that only people from their religion will go to Heaven, and also that they will all go straight to Hell, and are the worst of creatures, because such is true of all non-Muslims.
There are also ample explicitly exclusivist Hadith narrations, for instance:
Sahih al-Bukhari 3062
Narrated Abu Huraira:
...
The Prophet (ﷺ) was informed of that, and he said, "Allah is Greater! I testify that I am Allah's Slave and His Apostle." Then he ordered Bilal to announce amongst the people: "None will enter Paradise but a Muslim, and Allah may support this religion (i.e. Islam) even with a disobedient man."
Sunan an-Nasai 703
'Ubaidullah bin 'Abdullah reported that 'Aishah and Ibn 'Abbas said:
When the Messenger of Allah (ﷺ) was on his deathbed, he had a Khamisah over his face. When his temperature rose, he would uncover his face. When his temperature rose, he would uncover his face. While he was like that he said: "May Allah curse the Jews and Christians, for they took the graves of their Prophets as places of worship."
Above, we see that on his deathbed, Muhammad was cursing the Jews and the Christians. Regardless of how he started his false religion, he ended it hating everyone and everything else besides those obedient to him.
The dilemma presented above is typically reconciled in the minds of Muslims in one of two main ways.
First, they will assert that Surah 2:62 and 5:69 only refer to those who were formerly Christians, or Jews, or Sabians, and would later become Muslim. The problem is, those verses say nothing of the sort. Instead, they list Christians, Jews, and Sabians with the believers in Muhammad, then group them as unit sharing the same situation. Their purpose is clearly to make an ecumenical statement to unite all Monotheists who believe in the Last Day.
The second way these verses are reconciled in the minds of Muslims is by appealing to the doctrine of abrogation (Surah 2:106, 16:101) - which teaches that later revelations supersede earlier ones.
Chronologically, though, Surah 5 is dated as the 3rd last Surah ever revealed, having been revealed after Surah 2, 3, and 98, and it contains 5:69 - one of our ecumenical passages. Therefore, this response - which appeals to a frankly ridiculous doctrine within Islam, which only demonstrates how Muhammad was making things up as he went along - doesn't really solve the dilemma that this contradiction creates for Muslims.
Muhammad was inconsistent, and preached self-contradictory information on who is eligible to get to Heaven. He apparently said whatever suited him best at the particular time he was revealing any given chapter.
If he was aiming to ally himself with the Jews or Christians, then we would get something like Surah 2:62 and 5:69. If he was looking to rally his troops, suddenly only Islam is valid, everyone else will go to Hell, and everyone else is the worst of God's creation.
The fact that Muhammad's religion was inconsistent on even such a fundamental, vital doctrine as how one gets to Heaven, is yet another proof that he is a false prophet.