This goes back to the point that just because someone wants other to have the right to something, doesn't mean they want that right. Gay marriage for example. I don't need to want to marry a man just for others to be able to marry. The two are disconnected. That's what people immediately will believe though. In fact, there are Republican gay, lesbian, and bisexual people. Not as many as there are Democrats, but that should be obvious. Republican policies do not benefit, and actually actively harm, gay people. Why would they be Republican?
That's not to say that all Republican policies do that, so you can be a Republican and not be homophobic, but then it's extra important that you draw a line in the sand for your views. I'm a Democrat who owns guns and believes we need to be more careful with immigration (yet I still want Mexicans to come in freely, so see how it isn't so black and white?)