Well, the only real delineator between who's a furry and who's not is all in identifying as such.
My old friend Mr. Jaws (who also died very recently - F in thd chat for him), for example, openly has an anthropomorphic megalodon OC that be used a lot, but doesn't identify as a furry, despite his extremely close association with those who do identify as a furry. Even though he engages in a lot of "furry" or "furry-related" behaviors (e.g. has an animal-based OC, does role-playing, is an artist, also has a giant megalodon fursuit with stilts to exalt his height, etc.), he doesn't identify himself as a furry, and since identifying as a thing is the thing that makes one person a person ("I think, therefore I am"), that doesn't make him a furry. He just doesn't genuinely identify himself that way.
To do otherwise is pretty much the same thing as calling a femboy (someone who identifies as of the male gender yet has an effeminate personality and traits) a trans-girl, and vice-versa, however greatly escalated in how wrong and potentially socially-stigmatizing this example is.
If you feel like you identify as a furry for whatever reason, you are already a furry as a result because you identify as a member of the fandom. If you feel like you don't identify as a furry, then that's okay too - you don't have to identify as anything if you genuinely don't identify as something. Just try to be respectful about it and be supportive of how other identify and believe in, provided it also hurts no-one or nothing as a product of that, and is morally and ethically sound.
Hopefully this rant helps you out :>
