With the civil rights movement still a present tense affair and europe still in an imperial mindset, i dont know if there would be much of a gay rights movement as of yet. Though, i really dont know.

Aids does exist, Googer has touched on it, but compared to the real life trajectory of the disease it is still very much the 70s. 

As for using the LGBT movement as a springboard, you can probably use it but it'll have to be part of a larger movement. With civil rights as an open question, it would be difficult for such a movement to gain traction alone. But part of some larger liberalizing movement? It is doable.