I think that Nuc has it closer to the truth, Ky. Although it’s hard to separate all the elements that have gone into creating and sustaining western civilization (”civilization,” in brief), there are any number of elements of this civilization that are distasteful in the extreme to both leftists and some Muslims.
And both of these groups tend to millennialism (I use an implicitly Judaeo-Christian term) of a certain sort; that which requires active, even violent participation of the true believer in order to bring it about.
The eyes of both these groups are averted from the fact that the paradises-on-Earth envisioned by each are in various ways exact opposites and cannot possibly co-exist. Even if there existed only one dominant group of destructively utopian revolutionaries, the blood of Humanity would eventually run deep on the ground; it could be only worse with two or more groups vying for the prize. The worst of the present revolutionaries, the ones truly without humanity, know this.
Allow me to add that although many Christians are millennialists, the ones I know tend to leave the transformation of world to its presumably final state of peace, prosperity, and grace, to the transfiguring hand of God rather than the fallible and too-often misguided hand of Man. In the meantime they strive sincerely to do His will and obey His commandments, which are manifestly flouted by the utopian destroyers.