Religion itself is rarely the problem:- more of a problem is Organised religion.
With organised religion someone is in charge. And at some point there will be some one else who wants to be in charge (like the Chinese in this case) or religions split from the inside. How many different types of Christians are there now? How many different versions of the Bible (if it's the word of god only one can be right) Who is it trying to blow up all the Shia Muslims of late? Oh right, other Muslims. The Troubles ran along religious lines but was really about who was in charge.
"If you don't believe, fine: that's your choice. Is it really necessary though to insult and denigrate those who do believe, but do not encroach upon you in any way?"
Well that would be fine but it only ever happens for religions that are in the minority. You have people who say the US is a christian state, or Egypt is a muslim state, and they VERY MUCH want to encroach upon everyone. Just look at birth control laws or dress code laws for examples, or worse blasphemy laws.