The cats are one of the main attractions at my listing. I host long term guests who are often missing their pets back home but, even when I hosted short term, the majority of guests loved the cats and most mention them in the review.
Of course, I make it crystal clear on the listing and in my messages that I have cats. I even say in my house rules, do not book if you are allergic to, uncomfortable with just don't like cats. Occasionally though, you do get guests who choose to ignore this, because they like everything else about the listing.
I have had guests with cat allergies but, so far, none of them have had problems staying here because the bedrooms are spotless when they arrive. They just need to keep their bedroom door closed. The communal areas are large enough that they don't need to come into close contact with the cats. Still, I'd prefer not to have guests with cat allergies. I don't think it's fair to me to have to stress about their allergy when they could easily have booked somewhere without cats.
Far worse though is the occasional guest who is actually terrified of cats. This I find highly irritating. It's pretty uncomfortable to host a guest who screams or jumps every time they see a cat or asks me every five minutes if the cat is going to attack them. Having said that, those guests have always left feeling more confident around cats than when they arrived. My cats are very chilled though.
Now, my Easter egg question in the house rules, which every guest must answer, is cat related so they have no excuse whatsoever to ignore the fact that I have three cats. This seems effective in driving away the cat phobes.
I doubt that I have lost many bookings because of the cats, certainly not enough to make a big impact.
If I had to choose between my kitties and Airbnb, the kitties would win hands down.