Tell me what you think of this, then.

In my country, an landlord owner can not forbid pets in a house unless there are specific rules that completely prevents it (like an HOA imposition, where no animals at all are allowed in an apartment building); it was ruled by our Supreme Court having a pet is an unwaivable right the individual has.

(Yes, most people ignore this and just outright ban animals.)

However, the owner of a house can demand certain conditions to be fullfilled, in order for an animal to be housed there, like the animal being registered (ID chip), licensed (paid annually), vaccinated, properly kept (cages, terrariums or whatever necessary to accomodate, safely, the animal(s)), behaviour (a dog can not spend their time barking their head off, a cat yowlling, birds screeching) and for the guardian to assume full responsability for any and all damages the animal causes.

This part is legal and most people would run for the hills if they found such a clause on a leasing agreement, as for the moment they sign it, they are legally binded by it and failling to observe any condition is legal ground for breach of contract.