I wasn't actually trying to imply that we shouldn't tolerate homosexuality - I hope this was clear, otherwise I need to work on communicating unambiguously.

This was clear, yes. No worries!

I was trying to make the meta point that right-wing opinions don't have to be powered by hate, but perhaps they often are because people can't separate emotions and logic.

It is certainly possible that, in the territory, homosexuality is an existential threat. I believe the Westboro Baptists have a model that describes such a case, to name a famous example. A person who believes that the evidence favors such a territory is morally obliged to take anti-gay positions, assuming that they value human life at all. in other words, yes, there's a utilitarian calculation that justifies homophobia in certain conditions.

But if I'm not mistaken, the intersection of 'evidence-based skeptical belief system' and 'believes that homosexuality is an existential threat' is quite small (partially because the former is a smallish group, partially because the latter is rare within that group, partially because most of the models in which homosexuality is an existential threat tend to invoke a wrathful God). But that's an empirical claim, not a political stance.

Since we're asking a political question, rather than exploring the theoretical limits of human belief systems, it's fair to talk about coalitions and social forces. In that domain, to the extent that there are empirical claims being made at all, it's clear that the political influence aligned with and opposed to the gay rights movement is almost entirely a matter of motivated cognition.

To generalize out from the homosexuality example, I think it's trivially true that utilitarian calculations could put you in the position to support or oppose any number of things on the basis of existential threats. I mean, maybe it turns out that we're all doomed unless we systematically exterminate all cephalopods or something. But even if that were true, then the political forces that motivated many people to unite behind the cause of squid-stomping would not resemble a convincing utilitarian argument. So, if you're asking what causes anti-squid hysteria to be a politically relevant force, rather than a rare and somewhat surprising idea that you occasionally find on the fringes of the rationalosphere, then utilitarianism isn't really an explanation.

If you're looking for a reason to think that any given person with otherwise abhorrent politics might, actually, be a decent human- yes, you can get there. But if you're looking for a reason why those politics exist, then this kind of calculation will fall short.