There's no one, right or wrong way to be a furry, and there's no guard at the door giving you a test for if you can or can't be a furry, lol.
If you wanna be a furry, then go right ahead! Or, if you just like cute, anthro characters, then you just like cute anthro characters. It's all your decision, it's a fandom, not an identity. 
From my experience, stuff like Zootopia, Beastars, Brand New Animal, and Aggrestuko, are all stuff that many non-furries like, and they're consideedr pretty mainstream and popular right now so again, I really don't think they reflect on you as someone who is or isn't a furry. (Again, that's something you decide, not something the shows you watch decide.)
Like, do you wanna pursue original work with anthro characters? Is something boring if the characters aren't animals? Do you wanna make a fursona? Would you ever want a fursuit? Would you ever wanna go to a furry convention?
These are questions I think you'd wanna consider answering about yourself that would help you decide if you wanna enter the fandom at large. Otherwise, I think you just happen to like stuff that's popular right now, lol.
Hope this helps! Good luck!