I can't see how you can make this distinction. Have you ever had a college-freshman level Western Civ course? It's ALL about Christianity--from the rise of the early Roman Catholic Church to the Holy Roman Empire to the various schisms and heresies all the way up through the Reformation.
Western art (Michelangelo, Rafael), music (Gregorian chant, Palestrina, Bach), literature (Bunyan, Donne, Milton) and architecture (Leonardo, Wren) are completely subsumed by Christian tradition. In fact, they existed and developed solely because of the Christian religion.
It wasn't until the "Enlightenment" in the mid-to-late 1700s that Western institutions began to part ways with the Church to any extent--and even now, religion in the Christian world is as important a factor in its development as it is in the Muslim world.
I know you can draw many contrasts between Islam and Christianity, but you can also draw quite a few parallels. Islam was not ALWAYS the scourge and bane of the earth; there was a time when it was the repository and caretaker of the learning of the ancient Near East, and the contribution of Muslim Arabs in the sciences and mathematics is inestimable.
Of course, that was then and this is now. The poverty, ignorance and social backwardness of the Islamic world today has to be laid at the feet of that religion and especially, the "enlightened" potentates who use it to further their own ends, from Libya to Saudi Arabia to Iraq to Iran.
Let us engage the present threat, yes, of course, but let us not rewrite history to justify our doing so.
Inestimable. I keep hearing this line. All I ever heard that the Muslims contributed is the concept of zero and algebra. For me the discovery of the concept of zero is a bit overblown; it's like hearing mathematicians make a big to-do about null, nil, and the like. I'm sure even a caveman knew when he had nothing that he really had nothing. I recollect the Greeks discovered and developed geometry and formulae. By the way the Pythagorean theorem is an algebraic expression. So the Arabs generalized the concept. Big deal.
The Arabs contributed to medicine and astronomy? I think much of their medicine had already been discovered by the Greeks. I’m much more impressed with Kepler and Galileo’s venture into astronomy where the science is verifiable and results predicatable. Maybe the Arabs helped to maintain classical knowledge. I think the Eastern Holy Roman Empire would have done as good or better had they not been overrun and ravaged by the Muslims.
My big doubt about the value of Islamic contribution comes from the observation that Muslims pillaged and ran down the conquered until the earth lay barren. Every one of their nations now are devoid of accomplishment. How could an ideology as good as Islam wreak such havoc? Simple, it never was any good in the first place.