I'm not extremely knowledgeable on early communist China, so I'll focus on the USSR. Stalin made a concerted effort to eradicate the Russian Orthodox Church in Russia he went so far as to imprison priests, tear down churches, seminaries, and monasteries among other things. His hatred of religion mainly stemmed from the fact that his mother forced him into a seminary when he was younger, and Lenin's influence on him (and consequently Marxism's influence on Lenin). This attitude towards religion in the USSR carried on for a long time after Stalin died; as they did the same thing to Catholics in Eastern Europe in the 60's, 70's and 80's.
He basically just hated religion. He still didn't have any way to justify his acts beyond the material world. It's not like he can claim his murder is divine. That's where I step off of that issue though, because I'm not well-versed in the history of the USSR.
Basically I don't think Atheism itself was the main cause for the violence, but the various philosophies such as Marxism that call for a completely secular state caused violence for the same reason a Theocracy does. Both of those systems are set up in such a way that they can not tolerate religious diversity or else they would collapse. So yes Atheism can inspire people to violence; it's just done in a different way.
I would call for a completely secular state, in the sense that the government is completely secular, not that individuals can't believe whatever they want. It's good to see you realize theocracy doesn't need a god, look at North Korea. But theocracy is always a terrible thing, and most often it's based upon a religion.
I don't think atheists are terrible people as a whole, but I certainly would argue that faith or the lack thereof does factor into how a person acts.
I would argue that any claim that people of faith (or people of Christian faith) generally act more morally than atheists is based entirely upon personal ideas, and isn't backed up by fact or statistics. I really don't like hearing that faith makes people generally better, especially when the opposite is supported by the actual evidence.