Drawing them, no. Drawing a story where the anthropomorphic design is irrelevent to the story, no (just makes people suspect that you can't draw people). A story where the design clashes with themes explored or M rated material is involved, yes.
I don't think M-rated material has anything to do with it, since that can include violence.
I also don't think "clashing with themes explored" defines it, since that can include parody work.
Hell, Conker's Bad Fur Day is defined by the above two things and that's not really a game associated with furries.
"Furry" doesn't even really have a set in stone definition, even people in the furry fandom can't agree on what it is.
If you ask me, you're a furry if:
A) You simply identify as one and referring to yourself as one feels right to you. Also if you use furry related terms in your everyday lingo and see them as relevant.
B) You have an irrational bias for anthropomorphic animal characters and an irrational bias against humanoid characters. Yes, there are people like this, who automatically like anthro characters more, and humanoid characters less, JUST for being one or the other, regardless of actual quality of the character's concept/portrayals.
C) You are sexually attracted to anthropomorphic animal characters, specifically for being such and regardless of how sexualised they are in official material. What I mean is, I don't really call people who only find a very small number of anthros sexy. Usually when this is the case, it's because the character is EXPLICITLY designed to have sex appeal (e.g Krystal, Rouge, Lola-Bunny, Berri, etc). But if you find like, Sonic or Fox sexy, or a My Little Pony character sexy, then yeah I'd say that makes you a furry, even more so if you like to look at drawings of them with sexualised bodies (since you are then forcing sex appeal onto these characters when it doesn't exist to begin with).
These are at least three definite scenarios where the term "fury" is fitting, IMO.