Vanity Fair's Richard Lawson recently wrote: "I want a gay thing about gay adults who are relatively well-adjusted and aren't dying, that is wistful, hopeful, fun."
He's talking about films but I'll apply it to musicals. I can't define "well-adjusted" but as for the rest of the categories I'd put the following:
Boy Meets Boy (1975)
La Cage Aux Folles (1983)
Priscilla, Queen of the Desert (2011)
Tales of the City (2011)
[title of show] (2008)
A Year With Frog and Toad (2003) (it's canon!)
When Pigs Fly (1996)
threepanelmusicals.blogspot.com