Both being a goth and being a furry are about way more than clothing and appearance. Goths don’t really have anything to do with furries. I don’t know why you’re bringing them up.
Every furry I have met in real life thought it was a sex thing. Every normal person from the outside looking in thinks it’s a sex thing. Just look at the history of furry magazines and subculture and it is mind-numbingly obvious that it is a sex thing.
Even if it wasn’t a sex thing, would you want to discuss it at work knowing 99% of people will think of it that way?