Fortunately, my screening has limited my exposure to that.Some breeds of dogs are dangerous.

Roaches need: food, water, warmth, a secure breeding area.

In their email they "hope to adopt a breed under 50 lbs that will likely not reach full size before their lease ends." 

That said I know a lot of landlords who have run into issues with the ESA process; there's a difference between extra fees and cost to cover destruction of property, and as far as breeds, some insurance companies are a bit more reluctant to insure the property if certain breeds are residing there.

I also found out that you cannot restrict a tenant when it comes to breed Etc.

I see how many people struggle to find a place because of their dog so I wouldn’t have any breed restrictions, the dog just had to get along with our dog.

Success breeds success.  

@Rhonda SchmidtNormally, insurance companies do not accept pit bulls or other aggressive breeds.

I have them sign an additional pet addendum stating exact pet, proof of city license if required, shots, breed and age (no restricted breeds, no puppies), attest to temperament (no previous aggression shown), charge larger security deposit (refundable) if not already at state maximum, and have them get $300,000 in liability insurance instead of $100,000. 

Insurance-prohibited dog breeds require a $2 million rider on their required renter's insurance indemnifying the owner and management against those breeds actions.NOTE:  I LOVE dogs, and I totally understand that it's not the breed per se, but the owner or inbreeding puppy mill that will usually determine the dog's behavior.