Roughly 1/3rd of the House and Senate of Utah are BYU grads [1], and BYU is not the only religious Mormon university in Utah, just the largest.
Utah was literally founded as a state to be a place for Mormons[2], because they were a persecuted religious minority in other states. I grew up in Missouri, and part of Missouri state history is that of the 1838 Mormon War[3]. At one point the Governor of Missouri signed an order that paid out for the scalps of Mormons[4]. The aftermath was a mass migration of Mormons from Missouri to what became Utah, literally founded as a place for Mormons, to this day Mormons consider Independence, Missouri as a holy site, but Utah is the headquarters of the LDS Church and the predominant residence of Mormons in the US.
It is for all intents and purposes a theocratic state within the US.