In my opinion, the conflict between Conservative Christianity and gay rights basically boils down to a conflict over whether you believe homosexuality is biologically based or not. I do not think it is simply a case of close minded bigotry (though there are probably some bigots in most groups of people), but I think the reality is that a belief that homosexuality is innate is simply incompatible with literal interpretations of the Bible. In fact, it's almost on the level that the Theory of Evolution is incompatible with the literal belief that the world was created in 6 days.
If you look at the text of the bible, homosexuality is taboo. There really isn't much wriggle room there. If you accept that sexual orientation is innate, then you are left with a situation where a person is forced by their nature to struggle continually with desires that cannot be met. Up until early adulthood, this could just simply be described as going through puberty. However, conservative religious views have an outlet for these desires: marriage. Unfortunately that outlet is for heterosexuals only.
Going further, if you look at the biblical treatment of homosexuality, especially in the Old Testament, you are left with a situation where God went around smiting whole cities that supposedly went gay, and yet if homosexuality is biological, like hair color or height, then you are left with a dilemma since no one would want to worship a God that smites people because they have red hair or are over six feet tall. It wouldn't be defensible.
So what we have with denominations that take a more literal interpretation of the Bible is a situation where the theology hasn't really caught up to society yet, much like Catholicism used to be towards Theory of Evolution, or of a Heliocentric solar system. And so people who are in those denominations are basically in a situation where if someone says, "I'm gay, but I don't think I have a choice about it," you are literally putting them in a situation where they have to choose between acceptance of you, or acceptance of their faith, and most of them choose to continue to believe in their religion.