Hate to break it to you but the Mormon belt extends well up into Idaho (probably all the way to Montana on the East side) and down into Arizona, and diffuses out quite far from there. Probably need to go through Montana or skirt the Mexican border areas to avoid it, but border areas these days come with their own issues self created by our government...
I lived in Idaho Falls (well within the majority Mormon area that extends farther North at least to Rexburg) and never had an issue, but I definitely knew I was not part of the club.