Well, a lot of folks forget that as a Hollywood actor, and a former governor of California, Reagan was hardly a stranger to the LGBT community - his best friend was Rock Hudson, and his kids were nannied by a lesbian couple. He also vetoed legislation in California that would have prevented gays from working as teachers. Hudson and his husband were married in the White House, and both were pallbearers at Reagan's funeral in 2005.
While he didn't do enough to combat AIDS - and let's be frank, given we barely knew what caused it in the 80s, and we only really started knowing how to prevent it in the early 90s, and are only starting to treat it now, what the hell could have been done about AIDS in the 80s? - Reagan was almost a natural fit to advance LGBT rights, he was radical even by lefty standards of the day.
One of the odd effects was that gay marriage would come to politically divide the previously uniform LGBT community the same way that abortion divided the previously uniform women's movement, and along similar lines. The gays and lesbians that marry, settle down, and adopt a few kids all tend to be pretty firm Republicans. The young and single gays and lesbians meanwhile, tend to vote democrat. The old joke about liberals turning conservative when they get old and start a family applies every bit as much to gay and lesbian couples.
On the other hand, it did slow some other issues - much like abortion permanently divided the women's movement, gay marriage permanently divided the LGBT movement. It worked out for the best, given there were now groups on both sides of the aisle in favor of granting concessions to the LGBT community, but just like you have feminists excluding married women and pro-life groups from their marches, you've got some pride parades who exclude married couples, or view them as sellouts.
It also helped make sure the moral majority had some flexibility on social issues, allowing the GOP a firm libertarian streak, at least on LGBT rights. Without Reagan moving forward on gay marriage, would President George W. Bush have had the room to move forward on transgender rights? Who doesn't love the story of him going back to his college class reunion (Yale was all male at the time), and one of his former classmates had transitioned to womanhood. She was afraid to approach Bush, eventually telling him “You might remember me as Peter when we left Yale…" Without a seconds hesitation, in full view of the press, Bush answered, “And now you’ve come back as yourself." I may not be a fan of everything Dubya did, but damn if he wasn't a fundamentally decent man.
OOC: That first paragraph is all OTL. Prior to his presidency, Reagan had one of the best records in the country with the LGBT community. For a guy born in 1911, he was shockingly progressive on LGBT rights, especially for an era where multiracial relationships were controversial, much less same sex relationships. Not by our standards today granted, and he fumbled the ball in the White House, but you point out someone else born before 1911
who tells his kids that their nannies are lesbians, and that it's perfectly normal.
That
George W. Bush story is true too.