...shouldn't it still be a right?
Like the right to choose to bear arms? The right of an adult to choose to smoke or drink? The right of free speech? The right to choose to picket funerals to further a homophobic agenda? The right to choose your religion? Or non-religion? The right to choose between Samsung and Sony? The right to choose gasoline, hybrid or electric? The right to choose blue jeans or slacks? The right to choose Democrat, Republican or other? The right to send your kids to public or private schools?
Either way. It shouldn't matter whether homosexuality were a choice, environmental or genetic.
I suppose some of the above rights I've rattled off come with certain caveats. As pertaining to the right of free speech whereby it does not apply to the shouting of "fire" in a crowded theater. That the right to bear arms doesn't necessarily apply to concealed weapons.
Alas, homosexuality is not a choice. If it were, there shouldn't be any caveats like: you can be gay, but don't tell anybody; you can be with your partner but not in the same way that heterosexuals legally are; or as pertains to adoption, hospitalization or insurance benefits.
If we take religion out of the equation, what do we have? A non-issue! A big fat non-issue! Almost all the arguments against homosexuality and homosexual relationships hinge almost exclusively on religious scripture. Granted there are other reasons why someone may oppose homosexuality but I haven't explored that rationale and, besides, such opposition is probably so remote and minimal as to be a non-issue in itself.
This, I believe, is why many atheists have allied themselves with gay rights' causes and sentiment. It's discrimination based on a religious viewpoint.