I've allowed pets at my property, and it is well received. I love to take my fur baby with me when I travel, so understand how others do too. Touch wood, so far no issues with pets or damages.
We provide towels, bowls and poop bags, every guest has cleaned up the poop from the yard.
As far as pet allergies go, if someone is allergic to pet dander, I would assume they would not choose to book a pet friendly place so I do not worry about that possibility.
I do mention in my listing to keep pets off the furniture, however we all know this won't happen if a pet is used to being allowed on the furniture at home, so I ask the owners to bring a blanket for their pet to lay on....
I don't charge an extra fee for the dogs, I've built it in to my nightly price - so far only one person has asked how much is it for not bringing pets... I said no change, they didn't book but I'm happy because she was asking so many questions about the place that was clearly stated in the listing so I think I dodged a bullet with that one. I do however charge a $100 cleaning fee, it takes my cleaner three hours to clean for each turnover.
I think accepting pets if you're open to it is great, and as there's so few that do allow pets means my listing is shown to more people 🙂