Fair question and the Haidt reference below is quite appropriate.
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.
This is ********. No one said to "disregard their emotions", but simply limit where it applies. For example, Ceepolk can "be disgusted" by any argument(say about role of government) put forward by someone with whom she disagrees(say a libertarian), and doesn't have to be a part of that debate/discussion. But does that mean her disgust is viable reason to moderate the user in question?
Haidt's talks/papers/books all make great arguments for why the reactionary, emotional, and visceral reactions at A+ to even slight disagreement is extremely harmful and bad for everyone involved. You take someone who either 1) disagrees with a minor point, or a potential solution to an agreed problem, or 2) has different priorities than the majority of the group, but still agrees with the majority of viewpoints on the site; and then eventually, things come to a head and they are vilified and labeled "evil" or "racist" or "sexist" or a "bigot". Is there any suprise when people react negatively to this? Why they defend themselves? (Calling someone a Bigot is not attacking their argument, it is attacking the person, whether true or not). Then they are accused of "doubling down", and kicked out.
Why is the "outgroup" person's emotional response to being called a bigot/misogynist/racist not valid? It is totally understandable to react negatively to this.
To use a common A+ analogy. I step on your toes, be it accident or purposeful(irrelevant on A+, even though I personally disagree). Your response is to shout at me that I am stepping on your toes(totally understandable). Perhaps, I look down, I don't see your foot near mine, I don't see how I could possibly be on your foot in this case. I say so, possibly try to explain myself, or better understand the situation. Then either you or someone else also starts punching me on my arm saying "You are standing on his/her/my toes!!!1". My concern now shifts to myself being punched in the arm, rather than your toes, regardless as to if I've gotten off of them or if I've apologized or understood how I did so. Now, I am accused of making it "all about me" after several others have jumped in to punch me on the arm, and that I am derailing.
Is the fact that I stepped on your toes proper justification to you or others punching me in the arm? Is it not unreasonable for me to try to understand if I am actually on your toes, and how to better look out for toes in the future before apologizing? Is it not normal for anyone accused of something to first figure out if they did it(if they don't remember if they drank the last of the milk) or deny it outright(If I know I didn't eat your sandwich), or be very upset if I called names or insulted for something, especially if the person is using words in a way I am unfamiliar,(IE A+/FTB meaning of misogynist versus common understanding).
Can you also see how a productive solution is very unlikely in this scenario? How emotional responses, while real, lead to me being banned for stepping on your toes, versus any number of other people punching me in the arm? Why is it fine for someone to say "some white CIS-gendered dude" as a dismissive, but if(in a relative situaiton), I (or someone else) can't use "some asian trans lady" in a relevant situation. Both would be dismissing an author rather than their point based on some information about the group that the author belongs to.
I have no issue about someone background being brought up as to affecting their views, but when it is used as a dismissive or an insult, it should be reacted to the same way, regardless of which demographic the person belonged to. The less priveleged posters at A+ are not in danger of being silenced, The mods have set up a lot of ground rules. It is just obvious that the emotions of some are protected, while others are not.