@David969 I agree it's an irresponsible, ill-considered policy, broad based for Airbnb to avoid lawsuits—myopic at best. Because, ironically, it will end up backfiring on everyone , encourage intolerance, and in particular against those it is meant to protect, i.e. people who really do require emotional or therapeutic assistance animals for valid reasons plus it encourages and allows more abuse by guests - i.e. those who want to travel with their pets and lie about them being support animals.
Airlines are now limiting what can and cannot be regarded as an assistance animal (due to people abusing the system) and there is even talk of certificates being mandated to prove validity. That is one way to resolve it, but it could well become an invasion of privacy depending on how it is approached, as well as being an onerous burden to those who most need this kind of support.
The only clause in Airbnb policy that may apply to you is:
"if your listing includes a shared space and an assistance animal would create a health or safety hazard to you or others (e.g. allergies and pets who are unable to share space with other animals due to a safety concern), we will not require you to host the guests with the assistance animal."
https://www.airbnb.com/help/article/1869/what-is-an-assistance-animal%3F
Another problem is, even if your place says no pets (no animals) Airbnb forces you on pain of penalty to host them under this policy. This could well cause problems for other guests who booked expecting an animal free environment—thus the listing becomes inaccurate because of Airbnb policy. It's a catch-22 for a host. No doubt the guest would be refunded so again the host is forced to absorb all risk and be de facto free insurance agent for Airbnb.