ygetoff said:
The people who believe that they are right, and that everyone else is wrong.
Self-righteousness, according to Wikipedia, is a feeling of smug moral superiority (let no-one say I don't do my research). So I'll say it depends. How they feel about their own morality has no bearing on the rightness or wrongness of their position, or how hypocritical they are. I personally believe we're all guilty of a little self-righteousness from time to time, and as you say, we need to stand up for our beliefs. We just shouldn't go overboard.
The sentence I quoted confused me, however. I would quote at you from The Ragged-Trousered Philanthropists, but I can't find it, so I'll make it up myself. Doesn't everyone believe they're right? If I didn't think my beliefs were right I wouldn't hold them. Same logic applies to believing other people are wrong, assuming in this case that these are people who disagree with you. If you thought the people who disagreed with you were right then you wouldn't disagree with them.