@Jan186 If your listing is 'no pets' then stick to that rule. If you bend it for every guest who has a 'non shedding/small/timid/angelic/quiet/fastidious pet' (which they always are, by the way - no guest will ever tell you their pet is gigantic, loud, obnoxious, sheds like a son of a gun etc etc) then you may as well just be pet friendly. Airbnb does not do a good job of supporting pet friendly hosts, though.
I'll add, if you do want to ever claim for pet damage, don't mention the pet, just the damage. Also, if you're not going to accept pets, you will still get inquiries asking you to bend your no pets rule, so it's handy to have a saved template message to reply with. "So sorry, but as we are listed as 'no pets', we must adhere to that so that allergic guests may book with confidence."