I tell my family I post on the fediverse just like I mention most of my hobbies. Work, I wouldn't mention posting on here, but I would mention other hobbies.

But also, being a furry seems like its much more a part of their identity than like a casual hobby and would probably be more akin to transitioning. Adopting a new name, look, etc, including when meeting up with other furry friends (I've never been to a furcon, so only judging based on what I've heard from others). Some still use their birthname for those kinds of things, but for others their birthname might as well be a deadname in the context where they're comfortable being themselves.

Granted, many do hop from one fursona to another at some point or another, but gender fluid people exist too and many trans people go adopt new identities (like NB-> woman or woman->agender, etc).

There's a couple furry streamers I know who seem to be eggs and basically use being a furry as a way to express themselves (one seems to have internalized transphobia issues and the other seems to be agender and may just not realize that's an option or may think "trans" implies having a gender).