>>2 OP didn't say anything about atheism.
And either way, that's not what they're asking. Of course people kill people for their beliefs. It's more of a question of what part of religious beliefs cause people to use it as their reason to kill and how.
For example, the Oklahoma City bomber didn't just kill because he was a conspiracy theorist - it was because the conspiracies he believed in lead him to think he needed to take revenge. The affect a belief has on a person really depends on the topic, which is why OP specified religion.
>>1 With religion, most of these circumstances seem to occur because their beliefs lead them to think the world would be a better place that way. By oppressing and removing the sinners or unchosen, they can more easily lead their brothers and sisters to have better lives and afterlives. It's a way of working towards the greater good. However, religion in itself is usually about being virtuous each day with the little things instead, which is why many other religious people get frustrated when this approach is talked about like it's normal.
There are exceptions, of course, like the Crusades. The Crusades
were supposed to create a better world by re-gaining access to their holy lands, but undoubtedly, a large factor of that was revenge for Jerusalem having been taken from them.
