How do you respond to someone who calmly and civilly holds opinions about morality that are diametrically opposed to yours?
I start by asking the person what rational basis they have for their beliefs. Old fashioned dialectic is a great way to get to the bottom of disagreements of all sorts.
I could have a relationship with a man, and its moral; but my relationships with women are immoral. What changed here? Obviously the gender of the partners, but is that what actually accounts for the immorality? That part needs to be spelled out. I'm not asking for a lot here, if someone wants to call me immoral for being gay, I think I deserve an explanation.
Explanations are where things get muddy. Usually, immoral things are classified as such because they cause some direct or indirect harm to others. Someone's a victim, someone's an assailant. Its easy to see the roles in cases like murder, theft, rape, assault -- homosexuality, however, is the odd duck out. Its not obvious why homosexuality harms anyone directly or indirectly, who's the victim, who's the assailant? Why does the harm disappear by swapping out one of the partners for someone of the other gender, why do those victim and assailant roles disappear?
Opponents of LGBT rights are quick to say that being gay is immoral, as if it were obvious to everyone why its immoral. But its not. They're fond of comparing homosexuality to rape and murder, but nothing accounts for it harmful in any way comparable at all. (Quite frankly, if they think homosexuality is immoral in the same way as murder, it tells me they have not the faintest inkling of an idea why murder is wrong even in principle.)
If opponents of LGBT rights feel that homosexuality is immoral, they need to spell it out. Most of the time, they don't. Because they can't. There's no secular moral distinction between heterosexual and homosexual relationships.
So, the only thing we have to fall back on are religious arguments. This is the trump card, perceived as the argument for which no counter argument is possible. "God disapproves of gays, don't blame me for agreeing with him."
My immediate response then is to ask why god disapproves of gays. And now we come full circle. If God doesn't state rational reasons for opposing homosexuality, he cannot in principle state any rational argument against behaving otherwise. Its an absolutely startling revelation that, in absence of some explanation, there's no rational basis for obeying God in the first place -- except that God is bigger and stronger than everyone, and he'll torture you if you don't.
There are so many numerous problems with religious morality, most severely that religious morality is culturally relative. Its not absolutely in any way, shape, or form, it follows the social mores of the time. Religious texts are not an exception: they reflect the social mores and customs of the period and culture they were written. That's why you had slavery abolitionists and anti-abolitionists claiming to preach the will of God from the very same bible. Every contemporary issue from women's rights, animal rights, gender norms follows the exact same script. Religious prescriptions with good underlying rational basis, like prohibition on murder, stand the test of time; prescriptions without rational basis, such as
prohibition on men with long hair and women with short hair, are discarded.
If people don't oppose homosexuality for rational reasons, they must admit to themselves they oppose for irrational reasons. So then, on what rational basis can we draw a moral distinction between homosexuality and heterosexuality? We can't. They are morally equal.
Is there a point where your own deeply sincere opposition becomes hateful?
Only when someone says something incredibly hurtful, like accusing me of being morally bankrupt and a danger to children. I get worked up about the homosexuality issue because so much of the opposition is rooted in character assassination without a damn good reason.
I go to great lengths to justify things I believe, to make an effort to understand how others justify opposing beliefs. There are many times when I change my opinions on things. The debate on the homosexuality issue, however, is over. Its weighted lopsidedly on the side which states that its accepted, so much that there's no possible rational argument to the contrary.
I'd say the argument against homosexuality is comparable to the argument against evolution. Supporters have already won the intellectual and moral debate on the subject, the force of cultural inertia is the only thing pushing against it.