If, as Channel 4 would have them, Muslims ever did succumb to "higher criticism", then they would be mad, and indeed rather behind the times.
That strange and increasingly unfashionable thing, Biblical criticism, purports to read the Bible "as if it were any other ancient text", but in fact subjects it to a series of methods that would be laughed out in any other literary of historical discipline. Those methods are carefully constructed to "prove" the presuppositions of that strange and increasingly unfashionable thing, liberal theology.
Thus, if two Biblical books are word for word alike, as Matthew, Mark and Luke certainly are in parts, then they must have been copied from each other, since there is no way that God could have inspired them all and, funnily enough, done so in such a way that they confirmed each other's accounts. Hence the theory of Markan Priority, that Saint Mark's Gospel was the first to be written, and that Saint Matthew and Saint Luke copied out great chunks of it word for word. And hence the theory of Q, no copy of which exists anywhere.
Likewise, if Mark ends with what looks like a sort of synopsis of the post-Resurrection events recorded in the other Gospels, then that ending must be a later accretion, since there is no way that those events could actually have happened. Jesus simply did not claim divinity for Himself, so that rules out John at a stroke. Miracles simply do not happen, a position not even compatible with agnosticism. Style simply does not develop (seriously), so Saint Paul cannot have written several of the Epistles beginning with the words, "From Paul". And so on, and on, and on.
Academia is at last moving away from this sort of thing. When will the Church in practice, since of course She has never adopted it, and cannot do so, in principle? It is amazing that the account of the Ascension in Mark 16 is not the Gospel either for Ascension Day or for the following Sunday even in Year B. For that matter, it is astonishing that there are only Years A, B and C, with no Johannine Year D. Or, at least, it is amazing now. It was only too predictable a generation or two ago. But those days are, mercifully, gone.
If, like the Eastern Orthodox with whom they have always had considerable contact at ground level, the Muslims will have absolutely nothing to do with all of that, therefore continuing to believe, for example, that Jesus was the virgin-born Messiah promised to the previous Prophets, then good for them.