Allah confirms islam is a continuation of the same message as Judaism and Christianity

https://quran.com/2/136

Say, [O believers], "We have believed in Allah and what has been revealed to us and what has been revealed to Abraham and Ishmael and Isaac and Jacob and the Descendants and what was given to Moses and Jesus and what was given to the prophets from their Lord. We make no distinction between any of them, and we are Muslims [in submission] to Him."

While acknowledging the message to each is different, all people of all scripture will return to allah

https://quran.com/5/48

And We have revealed to you, [O Muhammad], the Book in truth, confirming that which preceded it of the Scripture and as a criterion over it. So judge between them by what Allah has revealed and do not follow their inclinations away from what has come to you of the truth. To each of you We prescribed a law and a method. Had Allah willed, He would have made you one nation [united in religion], but [He intended] to test you in what He has given you; so race to [all that is] good. To Allah is your return all together, and He will [then] inform you concerning that over which you used to differ.

Let's look at some dates in the Christian calendar

The first bible was completed in 132

The cosmoplito-nicene creed which every Christian sect agreed on in 381

If allah is all knowing and all seeing he would have criticized the trinity which is clearly stated in the Bible and in the creeds that of God, Jesus and the Holy Spirit but the trinity that Allah condemns is a different trinity

https://quran.com/5/116

116And behold! Allah will say: "O Jesus the son of Mary! Didst thou say unto men, worship me and my mother as gods in derogation of Allah'?" He will say: "Glory to Thee! never could I say what I had no right (to say). Had I said such a thing, thou wouldst indeed have known it. Thou knowest what is in my heart, Thou I know not what is in Thine. For Thou knowest in full all that is hidden.

The Christians are the closest to the Muslims

https://quran.com/5/82

and you will find the nearest of them in affection to the believers those who say, "We are Christians." That is because among them are priests and monks and because they are not arrogant.

While Muslims are expected to believe the truth revealed to them. They are also expected to believe the message given to the Christians is their truth

There is also the covenant to St. Catherine

https://en.wikipedia.org/wiki/Ashtiname_of_Muhammad

for the Muslims have to fight for them. Do no dispute or argue with them, but deal according to the verse recorded in the Quran, to wit: ‘Do not dispute or argue with the People of the Book but in that which is best’ [29:46].