The tenant is complaining about mold and that she has many allergies.  

I joked about that but the tenant has pet allergies. 

If you have allergy wouldn't you double check with a landlord before you rented a place just to be safe.I'm assuming he is going to say there is a allergy.How should l proceed?

On a serious note the pet's that you have on the premises as the owner doesn't obligate you to accept pets in your property, (though you may want to pet friendly rentals are always in demand) just know that having the pets on the property might make some renters think twice about living there if they don't like dogs, have allergies etc 

There are so many people affected with breathing disorders and allergies that majority of tenants LOVE these easy care, easy clean, dust-free floors. 

He and his wife have recently moved 7 hours away for his wifes health/ allergy reasons and do not want to manage the property long distance. 

Ok, so lets say a landlord had a building that was specifically marketed towards tenants who have allergies.

We share the same legal address, utilities and airways.In this specific living environment with a spouse that has been hospitalized with allergies due to pets, can we decline to accommodate assistance animals in our own home residence?

I have been able to buy Christmas gifts for children in need, donate supplies to families who were devastated by a house fire, purchase electric lawn mower for a home owner who had an allergy to carbon monoxide.  

There is mildew and many types of molds that are completely harmless, but there are a few that are toxic and all of them can be dangerous to people with allergies which is why you need to be careful.First thing you need to figure out is why you have it.