Well that may be a bit far. Unless you tried to pitch it as something from the medical lab went wonky when the world broke down and changed the character into a furry anthro
I can't say I think it fits with the vibe super well, in my opinion, but I'm not going to stop anyone, especially if the GM says it's okay. That said, you have to be ready for basically everyone to be on edge around you, and possibly even attack. Imagine being in the zombie apocalypse IRL and then you see an anthro animal walking around, wouldn't your instincts tell you that's an enemy?
You do make a good point. As I said it would depend on the context of what kind of furry it was full anthro or more nekko grew ears and tail from a science experiment that went wrong or something to that effect. But with it being more closer to Zombieland or Walking dead I am leaning more to say no to furrys