As an educated, informed theist, I want to give you a serious answer. Nothing I say is meant to be insulting. I mean the utmost respect.
After reading your question, it seems to me that you have a very relativistic understanding of morality. You said:
"You're still judging people for something they can't control and that's not even wrong except in your subjective beliefs that the rest of the world is not obligated to care about."
"Not even wrong except in your subjective beliefs". The problem here is that if what we believe is right or wrong is just subjective, and it is relative, then your belief that homosexuality ISN'T wrong is also just subjective. It isn't right, except in your subjective beliefs. So this is a problem. If what is right and wrong is just subjective, then it seems there isn't really any real truth to the matter.
But as a Christian theist, I do not think the matter is subjective. I do hate the sin, whilst loving the sinner (to the best of my frail human ability). I do not hate homosexuals, nor do I even hate homosexuality. You're right, it isn't a choice. Someone who is homosexual is born that way, and cannot help their feelings. What I believe is wrong is any sexual relationship outside of marriage, gay or straight. I do think homosexual activity is sinful, but I also think any sexual activity that is divorced from its proper context is sinful. But I myself have engaged in sexual activity outside of marriage, and so I am not in any place to make a judgment of someone else.
Finally, I do not think homosexual marriage should be permitted. Does this make me a bigot? Well, if it does, it also means that you're a bigot (remember, I mean no disrespect). Because if two people of the same sex should be allowed to marry because it wouldn't impact anyone else, then so should two close relatives. Two close relatives could marry without it impacting anyone else. Sure, their children have greater odds of having a congenital condition, but if that is the reason we don't permit close relatives to be married, then that means we should also not permit any two people to get married unless undergo genetic screening to make sure they wouldn't pass any latent or recessive genetic conditions on to their children. So, if we should allow homosexual marriage because it doesn't impact anyone else, then we should also permit incestuous marriages, since by the standards you're using there's no justification not to allow those as well. So by your own standards, you're a bigot if you doesn't approve of incestuous marriages.
But I would hazard a guess that you don't approve of incestuous marriages, nor do most people. And as I said, the reason isn't that incestuous partners are more likely to produce children with congenital disorder; its because incestuous marriages are wrong.
In sum, it is my view, and the view of many others, that immoral relationships should not be formally condoned by law. Incestuous relationships, and relationships between adults and minors are immoral and the vast majority believe that the law should not formally condone them. That would mean, by your standards, that the majority are bigoted against pedophiles and people with incestuous tendencies.
"I'm just a human being who thinks everyone should have basic human rights."
-This is one last thing I want to point out. All people have the basic right to have a relationship provided it is between consenting individuals who are intellectually and legally capable of consent. That is undisputed. What ISN'T a basic human right is a marriage certificate or a public official or preacher to say "I now pronounce you husband and wife (or wife and wife, or husband and husband)". That isn't a basic human right. Not allowing a particular group of people to get married for being of a particular race, ideology, religion, or sexual orientation is discrimination. BUT, no theist think that homosexual marriage should not be allowed for homosexuals for the reason that they are homosexuals. That would be discrimination. Theists who do not support homosexual marriage do not support it because they believe it is IMMORAL, not because gay people are somehow inferior and don't deserve equal treatment. Again, the reason we don't allow brothers and sisters to get married isn't because we're discriminating against incestuous people, its because we believe the incestuous relationship is immoral. That's the difference.
I hope I've made the theist position a little more clear for you. Take care.