I’m not sure whether I agree with that or not. In most civilizations throughout history, religion has played a fairly large part. But what about the Soviet Union? A basically godless culture. A miserable one, to be sure, but I think that was more due to totalitarianism than to atheism. In any case, there wasn’t anarchy nor were there people going insane (that I know of).
Godless yes, but they had BELIEF! I’m not a communism expert, but as far as I know they believed in the people, the state, the ideology. Unfortunately, none of the beliefs addressed what happened when they died. I think that’s the major part of the religion crutch – addressing the purpose of your existence (i.e. not random) and having somewhere nice to go when you die, even if your life totally sucked.