There was a new version starting in 2017 that specifically cast him as a gay playwright. But that was not the beginning of the trope, if I may so call it. Jokes about him fitting the gay stereotype started as far back as the early gay lib era (1969 onwards). He hadn’t been that popular a character compared to lots of other Hanna-Barbera characters, which could partly account for the number here who never encountered the trope themselves.
Bert Lahr sued and won against some commercials using the Snagglepuss character and voice, such that the commercials had to include the actual voice actor’s name (Daws Butler) somewhere in the commercial.