That's my point. Ours tend to be the types that can keep to themselves. Theirs are the kind that can't.
What? No. There is no kind of religious type that can keep to itself once it gets the power to start forcing other people to live like them. There are some kinds of religious, though, whose beliefs inherently prevent them from amassing such power. You're not going to see the Amish forcing anyone to live like them any time soon because their religion forbids them taking up arms. They don't have the means, and their lifestyle forbids them acquiring them, so it's not going to happen.
The only thing that stops any particular Christian sect from going bad (they all have the same book more or less, so they all can justify any kind of bad behavior if they cross their eyes just right when they read it) is other competing sects, and the fact that their numbers are all dwindling. The only religion growing right now is Islam, and IMO that's only because they have a large captive audience to which they can sell their story. Depressed people are easy targets for religion. Bring up quality of life in the places they're making inroads and you'll see them falter rapidly. Nobody happy needs religion.