I see it a little differently, De ... more in the way of which comes first or is predominate.
islam is a despotic socio-political system with some religious trappings intentionally built in so that it can masquerade as a "religion."
In any event, as you say, islam and Western Civilization (Classical Liberalism) are completely and utterly incompatible - period. Actually, islam is quite compatible with the tenets of the National Socialist German Workers' Party.

The essential American soul is hard, isolate, stoic, and a killer. It has never yet melted. ~ D.H. Lawrence