I've never seen a cat in a quilt shop...my boys are super fuzzy so I'm always worried about cat hair on my quilts. It's impossible for me to keep my quilts 100% fur-free and that's one reason I always wash them right before I give them away. I think I would still shop in a quilt shop with cats (since I pre-wash, have cats of my own, and no allergies) but I would probably check over the fabric pretty closely...my boys are PRETTY good but ever so often they get a hankering to put their claws to my furniture. I would check for snags just in case the shop cat decided to sink claws into a bolt or two when nobody was looking.
My favorite used book shop has a store cat named Booker and I adore that little guy. I always feel special when he comes to me for some attention while I'm shopping. He purrs super loud and will stand up on his hind legs to collect a head rub if I'm not diligent enough in my petting. I look forward to having a little "Booker time" when I go there - he is honestly part of the reason that I enjoy going to that store so much, even though I have cats of my own. So I guess it goes both ways.... I guess I'm just really really fortunate not to have allergies!!