The phrase "to butt out" means to stop interfering in someone else's affairs or business, usually by minding one's own business and not offering unsolicited advice or opinions. Full definition
And no, being told to butt out of other peoples lives and that you can't force your religion in to law is NOT persecution. (religion.blogs.cnn.com)
If you're a liberal city - slicker, you don't have a clue and have probably never hunted nor gone target shooting for fun, so butt out of our business. (religion.blogs.cnn.com)