Most people aren't uncomfortable with the idea of straight character with sexuality, if not an active sex life. Oftentimes they expect one. But a lot of people are made uncomfortable by the idea of a sexual gay character, and it's safe to assume that most gay people aren't celibate, and are sexual in some way. Using a celibate character doesn't address anyone's issues with gay sex or even the idea of a homosexual relationship in any way, it avoids all that, and thus you have characters who just happen to be gay, the way you might happen to have, say, run track in high school. It's a fact about you, but it has no real bearing on who you are as a person. That seems to be the case with Dumbledore. He's a noble, good character who happens to be gay. Great, that's fine. What he isn't is a noble, good character who has sex, wants to have sex with other men, or finds other men attractive. And thus even though Dumbledore's a gay character, nobody's forced to confront any prejudices they might have towards gay people in general by empathizing with him, although his fatherly relationship with Harry might help to prevent the common misconception that gay men are somehow sexually interested in male children and teens as a matter of course, which is certainly something worth pursuing.
I don't really have any problem with the character per se, but I find it a little dubious to think that any of this seriously addresses the problem of intolerance. I hope that makes sense.