You may not care. You may be a mature adult who has learned to tell the difference between enjoying a celebrity’s performances and admiring that celebrity. But Miley’s fans are mostly teen and 'tween girls. I can assure you a lot of them give a rat’s ass what she thinks. Quite more than a rat’s ass. Maybe a whole herd of cattle’s asses.
Miley’s attitude might change minds. No, not the minds of conscientious adults who have reasonably considered the matter, and not the minds of bigoted adults who are reacting to prejudice. But maybe the minds of young girls (and boys?) who haven’t been as exposed to tolerant attitudes and haven’t personally faced the issue of having a best friend out. Having someone they admire express a compassionate and tolerant attitude may give them the opportunity to consider the matter in a different light than they get in church and home.
Following on from what Irishman said, I would say that Queer Eye for the Straight Guy and Will and Grace have done more to advance gay rights in America than Lawrence v. Texas or any gay rights campaign. They’ve helped to bring homosexuality from society’s fringes to the mainstream and humanized gays and lesbians.
For all its done to poison us, MTV has also done a lot for gay acceptance. The Real World always has a gay cast member, and those little “True Life” and “I wanna be a X” minidocs feature a disproportionate number of gay people. I can’t vouch for The Real World because I haven’t watched it since season 1 when I was a kid, but otherwise they’re generally shown in a positive light.