How do you keep this gem of a character without looking like a mean author?
Distill the traits that you like, obfuscate the rest.
What is his defining trait? Is it a general lack of self-awareness? Is he covering his insecurity? Is he like the rooster that crows and believes he calls the sun? Or is he making up for lost time by embracing an "instant" identity with gusto?
Make it like a small side-mystery that isn't explained, but shows a consistent trait as the "key" to all the annoying behavior. Like an Easter egg.
Give him an arc.
It doesn't need to be big, and he doesn't need to be redeemed, but give him his own arc so he has something he wants and has to struggle or compromise to get (or he fails to get because of his behavior). The difference in giving him his own arc, verses making him the butt of a joke, is allowing him the room to process what happens and react to it. It changes him, or he pretends it doesn't change him. Give him that human moment where the reader will sympathize, then have him cover it up so the reader can hate him again.
Give him some foibles he doesn't think anyone else knows.
This one goes along with the arc, but these are shortcomings he is aware of. He is not handsome, so he is flamboyant. He is afraid of people so he creates a persona. He is not very smart or influential, so he is loud and spouts quotes from campy movies. He feels like a failure so he tries too hard.
The trick is to show the cracks in the facade. Unfortunately there is not a "deeper compassionate person" inside, there is only an immature and bullied child who resents not being wittier, prettier, and worshiped by all.
It's not that he is the most annoying gay man in the world.
It's that he's the most annoying Kylie fan in the world.
Take the touchy aspects, the ones that will get you into trouble, and turn them into esoteric extremes. Be weirdly specific about his fetishes and sexual preferences – especially if they are odd or extremely unlikely. He can only ever love Ecuadorian footballers, truly. And Canadian Mounties. But no one else.
Have him argue that such-and-such obscure actor from the 1950s is THE ONLY. And of course, the crazy-wall shrine to Kylie Minogue where he meticulously proves how alike they are.
a "good" character treats him kindly anyway
Whichever character is your virtue signaler, they are friends. This works even better if it's an unlikely friendship, or someone who would seemingly be put off because of his flamboyance. A religious grandmother, or a sour curmudgeon who doesn't have time for nonsense. Or if you need to go to extremes, an innocent child or a dog can adore him for no reason.
The MC doesn't get it, but the character who represents goodness or folksy wisdom just has a natural rapport with the annoying one. The reader sees there must be something more there. If you need to explain it, the virtue signaler can be aware how sour he is but choosing to see past it, or completely oblivious as if he's perfectly normal.