"'The Communists are atheists. They want no gods at all.'
Except for the State, which makes them theists."
Wrong. The State is man-made, and the Communists know it. A god is divine, and the Communists reject the idea of a god because they reject any form of divinity. They believe only in what is human and material. Therefore, they hold that a superior group of humans composing the State should make all the decisions for everyone else. They are not theists. Theism would threaten their system by persuading people that there are truths to believe in higher than a man-made State.
> The State is man-made
So are gods. Find one that you can prove wasn't just thought up by someone, and maybe you'll be on to something.