One of my 'duties' as a volunteer in a hospital is to check the knit/crocheted hats for the babies. One group of hats was full of cat hair. Some of the hair was actually knit into the hat. I tediously picked off what I could, and used a lint brush. I don't know that those hats actually made it to the kids. If you had a seriously sick child, would you want your child to receive a hat that had cat hair on it?
We frequently get fabric with an odor - smoke, musty, etc. The strangest odor was the fabric that smelled like vitamins.