Great question! Before I get into it, I want to provide a little context. I've talked quite a bit on here about different understandings of 'homosexuality' throughout history. How sexuality was understood and conceptualized has changed dramatically over the course of history, although not in a linear or teleological fashion. When we use words like 'gay' or even 'homosexual' we situate our discussion in a particular time and place. The 'modern' homosexual-gay-lgbt-queer movement has its origins in late 19th and early 20th century Europe, where Karl Heinrich Ulrichs, Karl Maria Kertbeny, Magnus Hirschfeld, and others began to create a framework, and some of the corresponding vocabulary, for understanding 'new' ways of framing gender and sexual identity. In the US, we often use the end of the Second World War as a kind of point of demarkation between earlier notions of sex, gender, and sexuality and the more current frameworks. For that reason, I'm going to confine my answer to that period. Although there was a vibrant (and remarkably open) homosexual culture in the US from the late 19th century to the 1930's, there are so many substantial and important differences that it would be both challenging and potentially problematic to compare movements.

The main organizations of the post-WWII pre-Stonewall era were the Mattachine Society and the Daughters of Bilitis. Mattachine was more male-centered, although there were some mixed chapters. DoB was entirely lesbian. Both organizations were formed in the 1950's, at a time of reactionary social-sexual attitudes. Whereas there had been a certain kind of openness allowed by the different social-sexual frameworks of the pre-WWII period, gay life in the 50's and 60's existed almost entirely in the closet. Although both these organizations were created to advocate for gay and lesbian people, maintaining the privacy and anonymity of their members was an extremely high priority. The Mattachine Society was named after a medieval French fraternal organization known for their masks; the name was chosen to indicate the need for homosexuals to be 'masked' from society. The name 'Daughters of Bilitis' was chosen because it was deliberately vague. Members were allowed to use just their first name - or a fake name- at meetings, and their publication The Ladder frequently mentioned that the identities of it's members would be protected (although this did not prevent the organization from being infiltrated by informants who provided the names of members to the FBI and CIA.)

Because of the strongly homophobic social attitudes of the 1950's and 60's, organizations like DoB and the Mattachine Society had a limited influence. They did make an effort to inform and educate the public about gay and lesbian people, but the extremely high social risks associated with homosexuality made any kind of substantial political organizing a challenge. Bars provided their own kind of organized community, particularly for working class lesbians, gay hustlers, 'drag queens' and other gender and sexuality outlaws. The informal (and usually underground) networks created in bars were often far more influential and important that organized groups like Mattachine and DoB (which were small, operated primarily in cities and by mail, and largely made up of the upper middle classes.)

After the Stonewall Uprising in 1969, there was a new kind of openness in regards to sexuality. People began to come out in large numbers, and new organizations were formed to lend a voice to this new generation. There was a flurry of activity in the couple of years after Stonewall, and this saw the creation of two organizations - the Gay Liberation Front and it's offshoot the Gay Activists Alliance. Both organizations came to be mostly dominated by white, middle class, cisgender gay men, despite the large number of trans* or gender-nonconforming people of color involved in the Stonewall riots. Despite some exciting action at the beginning organizations fizzled out within a few years, and failed to create a cohesive movement. That's not to say that there wasn't a lot going on in the 1970's. Gay men created impressive social-sexual networks in the 'gay ghettos' found in most urban centers. Lesbians became involved in lesbian feminism and lesbian separatist communities. The National Gay and Lesbian Task Force and the Human Rights Campaign - two of the most prominent national LGBT groups today - were both formed in the 1970's as well. Although they both played important roles in regards to lobbying and political fundraising, it would taking time before political and social attitudes towards gays and lesbians shifted enough for those organizations to gain real political traction.

The 1980's brought the kind of change that allowed political organizations to enter the mainstream. AIDS brought homosexuality into the mainstream consciousness in a way that nothing else had done before. Groups like ACT UP, Queer Nation, and the Lesbian Avengers were formed to draw political attention to AIDS and Queer issues, and brought a huge amount of visibility to LGBTQ people. By the 1990's gay and AIDS organizations really started to have political and institutional power. As gay became increasingly accepted by the mainstream, these organizations were able to broaden their fundraising base and expand their organizational goals. In earlier generations gay, lesbian, and trans* advocacy groups were small, kept afloat by volunteers and in some instances a handful of wealthy members.

When it comes down to it, organizations in the formal sense, played a pretty minimal role in modern LGBTQ movements. Informal community networks - although harder to trace - were hugely important in creating the movement.

That was a lot of information! I hope that at least kinda-sorta answered your question. And now for a brief list of sources: Odd Girls and Twilight Lovers - Lillian Faderman, Transgender History - Susan Stryker, Gay New York - George Chauncey.