IIRC tanuki is the japanese term for raccoon, actually. PETA is still nuts, though.
While it is true there is a real animal called a tanuki, it is actually a canid. However in this case we are referring to the mythological version of tanuki with the giant balls and related attributes it uses as drums (because it's goddamn Mario flying using a suit like it) and as such we can reasonably say it doesn't exist.
Also they're actually more or less sacred to Shinto Buddhism so asserting they're out there getting skinned is like saying Hindus eat hamburgers every day, so even if they don't mean the mythological version they're still goddamn insane.