If I may (not an opponent, but just throwing in what I see)...
I think homosexual relationships are seen like a poisoning of the social foundations of a few things. The first I can think of is the "assault" on the nuclear family unit as a picture, that culturally and politico-religiously (I think I made that term up), we idealize the mom, dad, 2.3 kids, white picket fence scenario as not a norm but THE family arrangement all should strive for. There is a small but notable portion of shaming to people who wish to remain single or divorced, couples who wish to remain childless, and families that choose to live in an RV and refuse to establish "roots" somewhere. I've even found a portion of shaming on families that choose willingly to have multiple generations in the same house, that aging parents who want to live with the grandkids are seen as "too attached" and not giving the parents their own space.
Grandparents are at times speaking up about
their rights to protecting and raising the children and usually are met with a lot of backlash.
The second thing I see in the opponents pov is that homosexual relationships also are squarely opposed to patriarchal designs for male power and control. In a heterosexual relationship, it's easy for society to assume who is leading the pair and asserts it's relationship with "head of household". But with homosexual relationships, it comes off as mass confusion as it tries to answer the question, "Who's in charge?" It literally forces us all to see egalitarianism as the baseline for finance, family, and specifically
love.
Finally, most of us are quite used to the war of the sexes. "She screwed me over." "Well, he screwed me worse." We're a culture that is filled with people who saturate themselves in the victim role, and love to rant about how we can't live with 'em, can't live without 'em. We love to complain about being stuck in our relationships but cite the "nature" argument that trying to live without the other is supposed to be worse than trying to live with them. Homosexual relationships puts a mirror to our faces and effectively tells us to shut the **** up and stop blaming the other...he/she is just as human as you.
I may be wrong, but it's worth a shot to try on their shoes and walk a mile.