I don't think it's an overwhelmingly religious issue. And many religions accept (to varying degrees) homosexuality. I'll grant that a greater percentage do not, though. The Episcopal Church supposedly allows gay priests (I'm not Episcopal, so not sure).
As far as limiting debate of morality to homosexuality.....I completely agree. The more frank discussions we have about contentious moral issues, the better chance that maybe we can solve them. Or at least come to some civil agreements on common ground.
If only people could speak rationally to each other about morality. Since morality is tied so closely to religion, or for those who aren't religious, to personal identity, discussions tend to get heated rapidly.
The problem is when this gets tied into the public sphere. For example, if government allows gay marriage, is it endorsing homosexuality? That's equivalent to pushing immorality in the eyes of many. One can make utilitarian arguments all day, but they are never going to convince someone who believes homosexuality is inherently immoral.
People have their own sacred cows and hot buttons. On top of that, they're often irrational. I've heard lectures about how gay marriage undermines the institution of marriage by a man who's been married three times. Must be the gays' fault.
On top of that, most religions have an evangelical side to them, i.e. they can't just stand aside and allow someone to descend into "sin." They have to "help" that person. This is usually a good thing, but in regards to hot-button issues, only aggravates the problem.
I'm a live and let live guy, but people who aren't make these issues very difficult to address on a rational basis.