I've seen "moral indignation," which might fit (though I think "indignation" still implies anger). I've also heard people who feel that way describe the object of their feelings as "disgusting" or "offensive," so you could call it "disgust" or "being offended." Of course, those people also seemed angry. Maybe the non-angry version would be called "bitterness."

As soon as I wrote the paragraph above, I felt sure that I'd heard "moral disgust" before. I googled it and the second link was this. I don't know about the quality of the study, but you could use the term.