He isn't gay, nowhere in the history or the canon of the DC world has he ever been gay.
In the last 20 years, he has gone from being a villain that respected women and children to be a woman abuser and a general asshole.
These people already have already heroed a bastardization of The Joker and Harley Quinn with Suicide Squad within the last few years. They shouldn't screw up one of the most iconic villains in comic book history because they can't get their own characters to make it to the level that they want!
https://screenrant.com/dc-comics-petition-joker-gay/
The petition cites Frank Miller’s interpretation of The Joker in The Dark Knight Returns, Grant Morrison’s interpretation of the character in Arkham Asylum: A Serious House On A Serious Earth and the opinion of legendary Batman artist Neal Adams as precedent. The petition also makes mention of behaviors The Joker engaged in that are “stereotypical” but paint a “very clear picture.” Specifically, that The Joker “… has many feminine traits – he uses lipstick, paints his nails, wears high heels and sometimes does crossdressing.”