Is there a word that means “a hatred of gay people”, rather than “a fear of or aversion to gay people”?

And similarly, why do we have words like “arachnophobia” which means a fear of something (not necessarily a hatred of it; though you might hate what you fear, that isn’t necessarily always the case, nor is the opposite always true either (fearing what you hate)), but “homophobia” is used to mean “hatred of homosexuality” rather than a genuine fear of it without necessarily hating it?

It makes me feel a bit sorry (as much as one can) for people who might genuinely be afraid of the idea of homosexuality, maybe even struggling with their own sexuality or possibly in denial of being homosexual themself, but without hating it at all (and being supportive of it), not having a word that conveys a fear of the concept/phenomenon without any kind of disdain for it, since “homophobia” would generally be interpreted to mean something far more negative. Usually when someone has a phobia for something, we support them to deal with it in a non-accusatory way, but in this case, well, I guess there isn’t even a word for that kind of phobia if it’s actually a phobia in the usual sense.