I think I understand one kind of homophobia. It's the kind that, as a bisexual male from a background that had some fairly conservative (and some contrarian and some old-fashioned moderate liberal) influences, has been the basis for a difficult and strong discomfort with myself that I only dealt with with difficulty. Wondering if that difficult path can be shortened and "given" to others in a way that lessens their homophobia.
First, the word homophobia is pretty awful; it's generally only a phobia when self-oriented; men in our culture are inculturated not to want to be gay, and are often goaded to do things in order to not seem/be gay. In that sense it's a fear. When aimed at others, it is not a fear; it's not that gays are feared (there is not a fear of gays beating one up), it's rather that they are placed into a mental category that I believe is biologically emergent (although the content of the category is not); that of being a freak and needing to be stomped out. I am talking unsupported theory here; that being said, I'll continue laying out the theory. I suspect that most species naturally police bionormativity, weeding out most genetic defects (using either deformities or abberant behaviour as markers of that); the oft-mentioned leaving newborns to die who have birth defects by humans living in tribal conditions is one expression of this. We may have managed to lessen the strength of this mechanism as we left our EEA and entered society; nowadays we try to have everyone survive and we can correct defective bodies (and occasionally defective brains, with meds and therapy, or at least institutions). Still, I believe that mechanism remains, and it's a category that, if it gets primed with certain things early in life, we'll respond with that almost-instinctual wrenching disgust and "stomp-it-out" behaviour. Even if it's people we love. Even if it's us.
I believe most of the politics of persecution of homosexuality is the outcome of enough people who have put homosexual behaviour into that box. How can we fix that? I suspect the strongest route is to never have the behaviour put into the box; just like with racism, regular and reasonable exposure to shows of same-gender affection prevent that kind of gut-disgust at non-heteronosexuality (and to the extent that nonheteronormativity also suffers this, the analogous solution should be sufficient). Fortunately, this is already happening, at least in the US. It won't help prevent people reaching an intellect-level set of beliefs against homosexuality, but I believe such beliefs would be far less harmful; they should not lead to violence in the same way that the gut-level instincts do given normal inculturation. For someone already raised, there may be limits to how much tolerance can be expected, and many people may come to an intellectual comfort with homosexuals without ever taming their gut; they may always be looking away at such displays while hoping the next generation won't have this inner conflict. Desenstivisation might slowly happen though. These problems will be amplified when that gut feeling is present in whole or in part in someone who is gay or bisexual.
We can expect this to impact politics; rural areas that don't have as much connection to national media will probably miss out on most of the content that helps keep homosexuality out-of-that natural category, and may remain dangerous for the non-heteronormative for the long future, long after all big and midsized cities in the US have reached nearly full acceptance.
If I am right on this, there is an upper limit to how far discourse can go with the gut-instinct-feeling person who doesn't accept gays, at least using logical arguments. My inclination, were I to come to the feeling that someone I were arguing with were like that, would be to try to pry at the strength of their general normative categories en toto; as I believe these mechanisms probably came about in tribal times when communities were tiny and likely relatively homogenous, it may be possible to weaken the entire mechanism by doing whirlwind tours of all of human variety in an attempt to exhaust one's comfort policing everything; everything from fetishes to interracial marriages to radically different cultural practices to styles of discourse, provided examples can be found that would trigger that mechanism in each, might do the trick. "Are you aware that there are people who do $thing, what do you think about that in this context?".
I've only done this latter technique twice, and I felt that I was making some headway but I wasn't sure if I really had it worked out what I was trying very well. Given that I can't explain it any better than I just did, there's some ways to go in improving it, but it's worth working on.
I suppose in a way, just like being an ex-libertarian, being someone who's struggled with self-discomfort on this issue might be helpful in letting me understand and instinctually think of ways to tackle issues like this. Maybe. Silver linings and all...