Hate to break it to ya - cat hair sticks to EVERYTHING!!! I have 2 gray cats, they aren't allowed on the quilts that I make and i am totally amazed at how much cat hair i brush off the quilts while I am working on them and how many teeny tiny cat hair balls are in the washer and dryer after i wash the quilt when i am finished working on it.
btw - dog hair isn't any different.