I just finished reading The Deviant's War by Eric Cervini and I would highly recommend it for anyone wanting to learn more about the political aspects of the LGBT civil rights movement in the 60s and 70s.
It focuses on Frank Kameny and the Mattachine Society of Washington DC. Kameny was a government astronomer who was fired and lost his security clearance for being gay. He believed that America needed to see that gay people were proper, respectful Americans who looked and behaved just like everyone else outside of the bedroom. He organized the first pickets and insisted that everyone wore business formal clothes, picketed quietly, with pre-approved signs, and displayed no signs of affection to their partners during the picket if they were present.