I agree that in some instances Harry has acted a bit immature and disrespectful. However...
I don't think he does it too often. Most of the time I think he's just challenging people's beliefs (justifiably).
He's demonstrated that he's an incredibly caring and selfless person, both admirable qualities. He's dedicated to making the world a better place, and is willing to sacrifice himself to do so. Shouldn't that outweigh a little bit of immaturity?
I was reading reviews of HPMOR on Goodreads and I noticed that the people who didn't like the book were essentially "put off by the rationality". They thought Harry was arrogant and condescending.
Then I was thinking, a lot of people are "put off by rationality" for similar reasons. What a shame. There's a lot of value in spreading rationality, and this seems to be a big obstacle in doing so.
Any thoughts on how to make people less "put off by rationality"? I think the core issues are: