Russia was despotic before, during, and after the USSR - and consequently before, during, and after an official state policy of atheism. I'm not sure Russia's political trajectory belongs in the religion pile.
China had an encounter with "Christianity" that didn't turn out too well (Taiping Rebellion). Mao's Communist Party was atheist and brutal. But like Russia, China has never known democracy or human rights in its history.
Probably we can conclude government entanglement with religion never ends well, and that includes both theocracies and efforts to forcibly stamp out citizens' diverse religious beliefs - one of the big things our Founders were right about.