Disgust, ethologists since Darwin and Richet tell us, is an emotion rooted in self-preservation. You have an instinctive aversion to tastes, sensations, and things that are likely to be harmful. (The history of the concept by Wilfried Menninghaus is worth a read, though it’s definitely the work of a Germanist.) Moral disgust, I suppose, is the same emotion projected onto an ideal body, the body of laws, habits and conventions that make us an “us.”
I find the repeated experience of moral disgust to be corrosive, and thus undermining of the supposed original purpose of the feeling. But there’s no way to let go of it. Perhaps it will outlive me.