Given that I find PETA to be generally offensive and manipulative, I wouldn’t look to them for linguistic correctness. As far as I’m concerned, “fur” works perfectly well when it’s still on the critter.
While my Vorpal Rabbit was certainly sweet and I loved him dearly, he was also incredibly destructive — A multi-year War Of The Wires, not to mention clothes, bookshelves and other furniture, bedclothes and pillows. Over six years later,I still have various possessions bearing the Mark Of The Bunny, not to mention the carpet damage. I don’t think I’ll be getting another bunny too soon….