Absolutely.
I could add that gay men who like cats are often the subject of a negative stereotype. Not so hard to understand given homophobia is rooted in misogyny.
When gay men are insulted it’s usually in terms of comparing them to women. So we get hated on for liking cats, if we like cats.
Actually, anybody who’s paying attention knows that gay men have something of a reputation (deserved or not, I don’t know) for being purebred dog fanciers.
From my own personal experience, I can observe gay men can be reluctant to be perceived as cat lovers — because of all the negative stereotypes you wrote about.
Personally, I have a dog and a cat. And I adore both of them.