She claimed that her daughter had some strange allergy to carpet and wanted us to rip out ALL the carpeting and put in all linoleum.

I have a tenant  has allergy problems. 

Here is my point:While it's true that some folks react to the mycotoxins created by live molds, most of the asthmatic and allergy-prone individuals who react to the presence of mold are reacting to the proteins in the mold body. 

Many younger renters prefer this as do allergy prone types.

Opens up the rental to people who have allergies and can't deal with carpet too.I've painted over wood floors and was sorry later, and then ended up stripping and refinishing.

We have laminate floors (no carpet) in that home BUT they have a dog (possible allergies maybe)        Another thing worth mentioning, vacancy for the above property is about $100 per DAY so i have to be thoughtful about this one.       

If the tenant has allergies, he would benefit from a HEPA filter.

However 1) He says he has allergies/sensitives to standard paint so he has requested a special paint.

Lastly, the tenant that brought the animal to our attention has bad allergies to dogs so the attorney has advised that we can deny the ESA based on these grounds.Thanks everyone for the feedback and advice.

We have had many prospective tenants ask about cats before stepping in for a showing due to allergies.