There was a really fascinating episode of This American Life about this, including first-person accounts from key figures and their families. It's certainly a storified retelling, but it's accurate, and well worth a listen. If you'd prefer something a little more academic, you want Ronald Bayer's Homosexuality and American Psychiatry: The Politics of Diagnosis.

In short, a lot of credit does go to the activists working both inside and outside the APA. External activists are certainly responsible for bringing the issue to the foreground on both a national scale and within the APA itself, and for opening the discourse between psychiatrists and gays who had never sought treatment for it. Internal activists are responsible for networking, and for the politicking that allowed the change to be ratified. The science wasn't exactly "new" in the early 70s. Evelyn Hooker's study - basically a blind evaluation of various gay and straight men, in which a third-party group of psychiatrists failed to identify the gays and found equivalent evidence of pathology between the gay/straight groups - was performed back in 1956. At the time, this was the first study specific to homosexuality whose subjects did not consist of patients already receiving psychiatric treatment. (Up until this point, nobody had bothered to study homosexuality in 'otherwise' healthy people.)

Can't believe I missed this question. Shit :(