Their narrative ultimately comes from the repressed conservative gay community. Conservative gay people, when they notice they have same sex attraction, do not conclude they're gay. They conclude that everyone must have these "temptations," and that gay people are just the folks that give into these temptations that everyone apparently gets. You explain away your same-sex attractions or desire to change your sex as a temptation of the Devil.

This is why seeing gay people in public doesn't have the same effect as seeing straight people, in their minds. Think about it like waves of copycat suicides. When one person jumps off a bridge, it inspires others to do the same. That's how conservatives view gay people being out. A gay person isn't someone that has a characteristic some of the population are just born with. Gay people represent those who have given in to the temptation anyone can have, and seeing gay people normalizes it and encourages others to give in.

It has the same logical coherence as "the only moral abortion is my abortion," but this is how conservatives view being gay. It comes from the lens of the repressed gay community.