RPGMemes

Depends on if the setting has a subculture analogous to and named "furry". For standard D&D probably not.

Do they have a Tabaxsona?

... would that look like a crude in-universe character sheet?

That's an interesting question. I think in the real world, being a furry is perceived as an off-putting fetish because anthropomorphic animals are imaginary. In a world where anthropomorphic animals were real, I think it would be relatively common for people to be attracted to them, so your character would probably just be considered normal.

Playing that character still makes you a furry. Sorry.