I think Utah is a bit more complex than that. As you note the LDS Church holds significant sway in the state, however like much of the Mountain West of the USA, the actual popular politics feature a combination of libertarian and socialist tensions rather than simple social conservatism.

Salt Lake City for example was the first major US city I encountered the audible cross-walk indicators for the visually impaired. And not just here and there, but all over the city. Salt Lake City has had popular gay and lesbian mayors and a vibrant and resilient collection of various sub-cultures that may not be desirable to the LDS Church but persist nonetheless.