People have the right to support homosexuality. People also have the right to not support it. Do you agree or disagree?
It depends on whether you’re talking about natural rights or legal rights, and whether the notion of support is defined strictly within the scope of individual liberty.
I would agree that people have the natural right to their beliefs as a matter of individual liberty, but I would not agree that people have the legal right for their belief-based actions to infringe on the legal rights of others.
In other words, it’s fine if you’re just another asshole who doesn’t support gay marriage, but that doesn’t mean you get to enact legislation to deny gay people the right to get married.