Mormons are having to deal with homosexuality. It may be that conservative, traditionalist people are better able to deal with something that goes mainstream. When the Supreme Court ruled in favor of same-sex marriage in Utah, the government told public officials that they might not have to sign marriage licenses for same-sex marriages, but that they would have to find someone who would. Would they rather have gays among them or break up extended families?
If anything, it is homophobia that presents itself as a cause for 'conversion therapy'. Violent homophobia is dangerous to potential targets (and one does not need be a homosexual to be at risk) and a great risk for criminal conduct.
Does anyone know what causes homosexuality, anyway?
This is a good Ted Talk on the subject. The theory is that pretty much everybody carries the gay gene, but it's epigenetics that cause it to be used in certain people.
https://www.youtube.com/watch?v=4Khn_z9FPmU