They don't anymore, but they certainly used to. The reason Salt Lake City is the home of the LDS church today is because they were forced out of Missouri and Illinois, and their extermination was officially authorized by the government. [1]
Wow, didn't know about that =). Although, it does say that:
> no one is known to have been killed by the militia or anyone else specifically because of it. There were, however, other associated deaths: the militia and other state authorities used Boggs' Executive Order as a pretext to expel the Mormons from their lands in the state, and force them to migrate to Illinois.
I'm pretty sure many muslims countries suffer much worse violence than that, over many more years.
[1] http://en.wikipedia.org/wiki/Missouri_Executive_Order_44