perhaps more specifically Islamic beliefs, but why?

Well, to fight superficiality, I guess.

On the Islamic part I do not agree. What the Islamic State does is pretty much textbook Islam. The problem is more that no decent human being (Muslim or not) would do this kind of stuff, except they are agitated for it by a hidden third party and convinced that they are doing the right thing.

What I also don't get when it comes to criticism of religion is that Communists were outspoken Atheists and Fascists usually insist on the distinction between church and state and see themselves as political, hence state and therefore non-religious movements.

That means: Religion seems not play an instrumental role in psychopathic group behavior - although of course the religious brain could confuse the teachings of Marx with the ones of Jesus or Mohammed. But erasing religiousness without at least testing the hypothesis behind it is brazen to say the least.