In my opinion, it depends on if Adora is really into Catra's furry nature. If she just loves Catra as a person regardless of her being a cat or not, she isn't necessarily a furry. If she decides she's really into Catra being a cat person as well as Catra as a person, she's probably a furry.

For example, I personally find furry characters attractive, but not more or less so than non furry ones. That might put me outside of societal standards for what is "normal," but I'm not really invested in "furry culture" enough to care for much outside of random posts on the internet that I like for other reasons. I personally think there's more to being a furry than enjoying hot fur people occasionally, so I wouldn't call myself a furry.

That said, these definitions are all constructed and shouldn't be stressed over