Not as much as Donkey does. I've seen him talking to waffles by candlelight. It's starting to creep me out.
Furries were around longer than that. Sonic SatAM was in 1993. Tiny Toon Adventures was in 1990. The Redwall novels started in 1986. And if you count Ranger Rick, a nature magazine whose mascot was a raccoon and he went on adventures with other animal pals, it started back in 1967.
How many Easter Island statues does it take to make baby Thumper cry?
(if you call Bambi "furry" for some ridiculous reason, then we'd say as early as 1942. Flower was cute, what can I say. And yes I know he's a guy... ok, shutting up now)