The inherent lack of logic of a belief system is irrelevant to the damage it can do to societies. Sin darkens the intellect; that a philosophical system fails by objective standards does not prevent adherents from believing it. (Also, I'm not sure why you're citing natural law; if radical secularism and Islam both ignore the natural law, why cite it as a point of failure for secularism and not for Islam? They both ignore the natural law, and justify their existence outside of its confines.)
As a case in point, the most murderous regimes in the 20th century have not been headed by Islamic tyrants, but by secular Communists so committed to their atheistic system that they think nothing of its contradictions or its limitations with regards to human nature: they would rather try to rewrite human nature with blood than admit they were wrong.
And besides: America has not been reduced to her current state because of Islam. Radical secularists - more pitiful than Muslims, being fools who proclaim that there is no God at all - have rendered a once virtuous nation into a cesspool of derangement.
There's simply no comparison.
We agree to disagree?