Store owners do things that alienate customers ALL THE TIME. Catering to one group often alienates another.
I recently took up archery, and one of the two local archery shops is very hunter-oriented. Everything in their shop, from their logo & decor to the practice targets you shoot at, has to do with killing animals. I'm a vegetarian and animal lover, so this bothers me. So, I go to the other archery shop, which is further away but has standard bulls-eye practice targets and seems to cater more towards the hobbyist. Should shop #1 stop catering to hunters in order to suit me? No. Is their business suffering? Doesn't appear so. They appear to attract plenty of customers who DO like to hunt with bow and arrow. That's the demographic they are catering to.
I believe there IS a demographic of people who enjoy animals in shops. I'm one of those people. All things being equal, a shop with a cat gets my business more than a shop without, because I really LIKE animals and for me, visiting with the shop cat (or dog) makes the shopping trip extra enjoyable. (This assumes a certain amount of housekeeping; I do agree a litter box odor is not going to encourage me to return; but that's true for any foul odor regardless of the source.)
You're never going to appeal to 100% of the population. A business owner has to constantly gauge interest and it's always a moving target. If I had my own used book store (a perennial fantasy of mine) I would DEFINITELY have a store cat. Those decisions are one of the perks of being a business owner! For better or for worse.