Atheism isn't a philosophy or moral system. There's nothing to entertwine with communism. A communist can be an atheist. So can a capitalist. That doesn't mean an atheist is a communist or a capitalist. You can't predict accurately really any belief system based on atheism because it's purely a lack of belief in god(s). Anything else thrown on top is a completely separate issue, which is exactly why you can find wild differences between us.