I don't really have standards in that topic. I can play games I have a moral opposition to. But it doesn't mean I ignore what I'm opposed to.
There's a lot of stuff in Yakuza and Persona games, for example, that I have disgust or dismiss for.
Treatment of certain characters of a certain gender/sexuality/identity, or general moral stances that I think are mind-numbingly stupid.
But I think that's part of appreciating art. Appreciating the good, discussing the bad. Not excusing it, not ignoring it.
Discussing it. With yourself or other people.
It's one of the reasons I don't like censorship. The, in my opinion, bad aspects of Persona/Yakuza, are a part of it, and I want everyone to see it, discuss it, shit on it, or praise it.
Anyway... I never really dropped a game because of a moral difference.
But I can see why people do.