The next gay bar in a humorous piece should be the one in the “Bar Scene” sketch by The Committee (1964), an American improv satire group, but I don’t have that album, though you can read a little more about it here:
So the next chronologically is this:
“The Realist”, November 1964
No actual homosexuals in sight but; “I’m trying to get the place known as a homosexual hang-out”?
The idea of gay men as scene-makers is a cliché. Even by the early 1960s there was the assumption that hairdressers and interior decorators are gay, and who knows how many artists and writers are “that way”. But 1964 saw the publication of Susan Sontag’s essay on “Camp”. Even if you weren’t a reader of “The Partisan Review” where it originally appeared or high-brow collections of essays, Sontag’s point was disseminated in reviews of the book and then became the buzzword in numerous newspaper and magazine columns. The new artistic mode was “camp”, but worse, Sontag also pointed out that homosexuals were its arbitrators and vanguard. Homosexuals were recognised as being in a position of explicit culture power. It is amazing how many book, theatre and art reviews in late 1964 and early 1965 push back against this, finding the flimsiest opportunity to criticise the idea of “camp” and to knock homosexuals (immature, developmentally retarded are the nicest arguments) in the process. So I think this may be what prompts this cartoon.