Quora Answer : Why do people want to enforce their religion on others?
Often religion is used as a cover / justification for advancing a political agenda. It's used to stop women having abortions. To confuse the teaching of biology (and likely in the near future climate science). To motivate people to go to war and fly planes into buildings.
"New Atheism" of the Dawkins or Hitchens varieties only appeared as a reaction to the increasingly visible political effects of strong religious beliefs.
If religion was just about who you prayed to and the clothes you wore, it wouldn't be an issue and few people would care about persuading anyone of anything. But because the patterns of belief shape the patterns of power in the world (remember when Christianity took over the Roman Empire?), people try to martial faith as they would any other weapon.