This has been a subject that has been debated for as long as I can remember; whether or not to allow your tenants to have pets. What I have always found, is that it really doesn’t matter what your policy is. They are probably going to bring them whether or not you actually allow pets.
When I bought my first couple of rental properties, I was very clear that I didn’t want pets in my houses. I didn’t want to have to replace the carpet after each tenant because of pet damage. It was always in the lease, and I always discussed my policy with the tenants. I learned pretty quickly, that there is a segment of the population that will agree to anything in the lease while they continue to do whatever they want to do.