Short answer: as something that should be considered when forming my own values, when discussing collective values and when talking to them about their values.
I see no reason to disbelieve someone's claim of visceral disgust. It exists. Their disgust affects and shapes their experience. It matters. In the real word cases I've seen, that disgust isn't feigned or is an reasonable response based on that person's experiences. It's valid. That disgust influences or even determines their beliefs about how they and society should react to people. And that emotional reaction ought to determine their morality.
That disgust is likely to convince them to adopt principles I strongly disagree with regarding how they treat gay people and what laws society should adopt. But arguing that they should disregard their emotions is a bad idea for two reasons, first they are likely able to simply couch their objections in "purely intellectual" terms. Second, I am unlikely to change someone's mind when I've taken their basic motivation out of the discussion.
I agree with everything that I didn't change to blue.
But... I find myself waiting for a conclusion. You seem to have painted yourself into a corner here. You don't disregard their emotions, but what do you do?
You could accept the primacy of their emotions and give up the argument. No gay marriage; it would upset the emotions of too many people! But I don't think you're advocating that.
You could accept the importance of their emotions, realizing that they are contradictory to your emotions, and stop there. A stalemate that by default preserves the status quo. (Except, perhaps, locally in enclaves where the people who share your emotions predominate by force of numbers.) But I don't think you're advocating that.
You can decide that, since the dispute exists on an emotional level, it must be contested and resolved on an an emotional level. So, time to pull out your own emotions like so many Poké Balls and do battle. Emotional tug-of-war. Emo a emo. Outrage, I choose you! If they can be disgusted by gay sex, you can be even more disgusted by their bigotry, and if you manage to show it convincingly, you win!
And that, I
do think is what you're advocating. Or if not you, many others in the A+/FTB sphere. That's why abusive language (as long as you're abusing the
right people) is so cherished and "tone policing" is such an ultimate sin there. Trying to win this kind of emotional duel while being restricted to civil discourse would be like trying to win a hog-calling contest without waking up a sleeping baby.
And practically everything that neutral observers have objected to about how things are done at the Atheism Plus forums and FTB and other A+ enclaves is consistent with that. Throwing would-be allies under the bus for minor or purely imagined transgressions? Biased and capricious moderation? Intolerance of any alternative view no matter how moderate?
That just helps show how powerfully emotional we are!
Well. You're not going to like what I have to say in this next part.
There's a name for that kind of emotional approach to argumentation, where the goal is to establish the moral superiority of your position by demonstrating how strong your own emotions are. It's called a
tantrum.
Tantrums are very effective at some things. They get a lot of attention, from your opponent and from anyone else within earshot. They're noisy and memorable. They blow off a lot of steam built up by frustration. They assert your identity which for some will be a new and worthwhile experience.
But... they come up a bit short in the long-term-effectiveness department.
And yet, a better answer of what to base your argumentation on is right there in the first sentence of what you wrote, that I quoted above. Values.
Values are not emotions. They can be informed by emotions; they can be and often are also misinformed by emotions. Fundamentally, they are not directly tied to emotions; they are based on ideas or principles or judgments, and they can and should be evaluated and informed by reason.
Meaningful change means expanding the Common Ground.
Myriad said:
As difficult as expanding the Common Ground is, there are many ways to do it. But the most effective way, judging from history, is to work from inside the Common Ground outward. The key is to identify underlying principles already agreed upon, and apply them in new ways to matters not yet agreed on.
Emotion won't get you very far in that process.
Respectfully,
Myriad
is underrepresented in both arenas, so imo deserves special attention. And as others and Myriad again notes, productive communication begins with finding common ground. The irony is that there is so much of it between the two camps, yet some choose to focus only on the rather minor differences-many just semantics-in perspective. 
