Nothing like finding cat hair in my food or on my fabric! That would be a deal breaker for me and I don't have any allergies.
My dog is the non-allergenic kind and doesn't shed so no problems. She only comes into my sewing room if i carry her in and put her on a blanket...otherwise she sits at the doorway on the carpet. Flooring is too slippery for her liking.
I'd stick with a fabric store that has no animals roaming around. Same with cig smoke....that's worse than animals in the store in my opinion.
How do they deal with the cat box odor permeating the store?