If that was true, they could win these fights legislatively and not
have to resort to the courts
It is the courts, typically, that pull the righties up by the pubic
hairs on these issues. They try to pass or maintain homophobic laws, but
usually the courts tell them to go **** themselves. But not only, and
only fairly recently.
Again you avoid the point. A majority of all Americans are not in
favor of gay marriage, (D&R).
BTW libertarians are in favor of everyone's rights but they are a
minority too.