Its ironic - muslims vigorously defended Jesus during the 'Last Temptation of Christ' kerfuffle years back. I heard they consider Christ a prophet then and recall wondering why Christians never fought that energetically to defend their faith.
I'm sure one day soon we'll have no choice.
The Muslims considered him to be a very important prophet (just not
quite important enough, and not the Messiah), but also one who never married, etc. There isn't any quibbling with them over their beliefs, after all, "it is written" in that case means not only is it part of scripture which shall not be changed (at all) under penalty of death, but also implies that it was very important, by virtue of being written down.
In Islam Jesus (Isa ibn Maryam) is considered a prophet (which is why they consider Him Muslim, because He couldn't be a prophet if not Muslim, now, could He?) who was born sinless and who neither wed nor had children, who spoke as an infant, healed the sick, cast out demons, and raised the dead as well as breathed life into inanimate objects (a bird made of clay).
The Last Temptation of Christ defied that account, and thus, defied Islamic teachings--and pretty much the New Testament accounts as well.
The salient difference is that to defy the Quran by any alteration is to change the scripture, a grave sin against Islam (the penalty for a Muslim is death), and Muslims take such things very seriously.
Christians endure such nonsense much more passively, and likely that is what the Muslims found shocking.