It depends on how well the author represents the character. If the character is a Gary Stu, Mary Sue or some non-binary "I am always right and win" type character... then it'll get old and stale fast and there is no point reading.
If the character has different ideas than me, but his or her or they're ideas are challenged greatly, and they have to consider the caveats and other things around their morals, then I would still love it.
I'll give you an example, Spider-man and Batman both have a no kill rule. When I was playing Arkham Asylum, I was upset at the idea that the villains Batman doesn't kill, go out and kill a lot of other people, yet Batman just puts them back in jail. You would think you'd hate that your ideals clash, but as you play it more and more you realize... just how hard it is for Batman to keep to his moral fiber despite all the shit that hits the fan.
It's the same with Spider-man. Losing the one he loves and still forcing himself to do the right thing. I don't agree with his morals, but the fact he suffers, the fact he pushes through no matter how hard it is makes the entire theme extremely compelling even if I don't agree with how they handle everything.