I think you greatly exaggerate the perception - from my experience in Texas- that Mormons are to be feared for wanting to cut off heads of unbelievers. Houston, Dallas, Austin, and El Paso included. Might be some resentment (of anyone) in deep East Texas woods like Liberty or Woodville, but certainly not medium to larger towns in Texas.
I do exaggerate a bit, I'm sure. But maybe not as much as some may suppose.
While anti-discrimination laws and such will keep a damper on various feelings of unkindness, they are still far too common. Mormons are not generally to be feared over any threat of physical violence. But to some sects, Mormons present an even greater risk: the risk of drawing away "real Christians" into a cult such that those Christians lose their souls by being tricked into worshiping the "wrong" Jesus. And it isn't like the incidents involving the Polygamous FLDS in Waco did much to engender even mainstream Mormons to many who are still not quite sure that the LDS Church ended the practice of polygamy some 100 years ago.
This is, of course, mostly off topic, and mostly in good fun on my part, except to point out that when I suggest a business owner in the South be legally permitted to engage in peaceful discrimination that I and others find offensive, it is with full knowledge that said business owner may very well apply such discrimination to me and mine. It isn't like I'm just ok with the other guy being denied service while I presume I would never have an issue. I believe there are a few, rare business owners who deny service to me on pretty much equal basis to those rare, few business owners who would deny service to Muslims or any other minority group.
To paraphrase something Jefferson supposedly said about mandatory education: I think it is better (at least in 2015 and the future) to tolerate the rare case of a business owner discriminating, than it is to give government the power to prevent all such discrimination.
On some issues, my libertarian side pokes through a bit.
Charles