Cat hair on quilts is a big reason I had DH build me a place for the Long Arm that can be completely cat-free. I've got nowhere in the house that I could put it and have a closed door (it was in the dining room).
However I've got to stop laying floppies out on the bed unless I take off the comforter first. The cats sleep on the bed and the comforter is full of hair. So hair gets on the back side of the floppy.
if I am gifting a quilt, I bring it in from the LA and bind it, then wash and dry and it goes into a bag.