The thinking that leads to religious persecution seems to go like this.
1) Our beliefs are true, and others are false.
2) Whether you accept our beliefs or not determines whether you go to heaven or to hell.
3) The people who promulgate these other religions are putting other people's souls in danger.
4) Even if we have to forcibly stop them from so, we can prevent them from leading other people on the road to hell.
5) Therefore, the use of force in the name of religion is justified.
However, you should notice that none of the other statements on this list follow logically from 1. The problems come further down the list.
Religions don't kill people, people kill people.