It seems you first have to guide people into realizing that they can't just consciously change what they instinctively cringe about, before they'll accept any argument about what they should be consciously scorning.

But you can consciously change what you "instinctively" cringe about. Otherwise, people couldn't, say, get over their fear of public speaking.

Sure, there might be some things you can't change, but one's moral views aren't really one of them. (Consider, e.g. all the cultures where killing someone for besmirching your honor is considered a moral good.)