In Super Mario 3D Land and World, whenever Mario, peach, Bowser or Toad use a super leaf, they turn into a Racoon-looking animal called a "tanooki", which they all share, and was not an animal until then. It is not any of their OCs either, it was just an unknown animal.

But Luigi? Luigi is kitsune. They even made a Luigi kitsune plush for him (attached image).

Cosplaying, you could say, as an already existing furry animal. Why did they do this with only Luigi?

This year they did multiple arts of the characters in costumes; toad is a ghost, mario is a pumpkin-guy, and peach is a witch.

Luigi is a werewolf. Cosplaying as a "furry" animal once again.

Not too much of evidence, but Luigi acts like a furry. For example (remember not all furries are like this) in some games it seems like it's hinted that Luigi... enjoys sexual touching more. ESPECIALLY in Bowser's Inside Story, he makes a "wooaah" noise when stroking two characters, one in the butt (there is context for it, he did have a reason)

I'm looking for more evidence, so stay tuned. Feel free to comment some of your own evidence in the... comments