said the Lord...
said the Lord: I am full of the burnt offerings of rams, and the fat of fed beasts; and I delight not in the blood of bullocks, or of lambs, or of he goats.' Since the temple at Jerusalem was lost in the seventh decade of the Christian era, there has been no sacrifice in rabbinical Judaism. In Christianity, the sacrifices of the Hebrew Scriptures are considered as types prophetic of the sacrifice of Jesus on the cross, after which no sacrifice can take place.
The sacrifice of Jesus is either re-enacted or remembered in the Eucharist where the bread and wine are blessed and thought to be, contain or represent the body and blood of the sacrificed Jesus. The vicarious sacrificial death of Jesus on the cross is thought to be an essential requisite for the forgiveness of sin. Muslims have generally, but not universally, denied the crucifixion altogether.
Obviously that is a stand the Bible does not share, since the crucifixion is definitely maintained in the Gospels. The substitution theory, known from the Gospel of Barnabas, does not seem reconcilable with the canonical Gospels. The swoon theory, whereby Jesus was crucified but did not die, is somewhat more tenable, but requires the assumption that the disciples were ignorant of the true facts. What is in conflict with Islam is not the death and resurrection of Jesus as such.
It is the vicarious sacrifice for sin which is absolutely and altogether unacceptable. The easiest and most direct path to that goal is merely to deny the crucifixion altogether. But in so doing, the Muslim must reject the Gospel narrative. The Christian doctrine of the vicarious sacrifice of Jesus has only two Biblical sources. The first is the allegorical interpretation of the sacrificial system of the Hebrew Scriptures.
The second is the metaphorical application of the Paschal lamb to Jesus in the writings of Paul and Peter. There is no Gospel justification at all. The only condition for forgiveness in the Gospel is in Matthew 6:14-15. We are forgiven as we forgive others. The Christian doctrine, despite being so central to the faith, has only the most tenuous Scriptural foundation.
Although Muslims do not do so, they could find a far firmer basis for their rejection of a vicarious sacrifice for sin in Scripture than the Christians find in favor of their doctrine. I shall not discuss further the historicity of the crucifixion and resurrection of Jesus. Some of the non-canonical Gospels do not even mention it.