If arguments appealing to your sense of fairness and the universiality of human rights don't do it for you, there is another reasion: Stick it to the Mormon Church.
My mother's side of the family are Mormons, and some of them, who I dearly love, are straight up bigots. That's my issue to deal with. But the LDS Church itself hasn't gotten directly involved in politics since they worked to defeat the Equal Rights Amendment. Fuckers.