Those laws actually seem to make it more likely that people with severe allergies might organize themselves or gather online to discuss how to find places to stay. 

What can I ask in terms of how to carry the animal around to prevent anyone else complaining of allergies and such?

(I do not know if she has a legit letter or not) Regardless, I understand FHA I can't deny her application based soley on the ESA, but if the one of the current tenant have allergy issue, can I deny then?

I had a similar conversation with a tenant, complaining to me that his allergies were worse...I was like, well, this house had brand new carpeting throughout when you moved in, but most people with allergies don't chose a house that is carpet throughout, and live with 2 dogs who shed so much they will clog the air filter in a month, and told him about plug-in  air purifiers, since the furnace isn't designed to clean the air, only to heat it, and those high rated filters are bad for HVAC systems according to any HVAC guy you talk to.

As for carpet, it might be a geographical thing but it is truly heartbreaking to hear a buyer say they're going to have to tear out all your new carpet because they have allergies or it catches the dog fur or something.

The contractor may have had allergies and just not wanted to do the job. 

Anyways, our contractor was first going to tackle the water issues and then knock out every wall (which I would have requested anyways lol) as nearly every wall visibly had mold and I am highly allergic to mold.In fact, even though I suited up I'm now having to go see my eye and health doctors as my eyes weren't 100% corrected and now I'm having allergy issues due to doing just a quick walk-through.So while you may think it is a scam, people like me literally need to have the job done fully and at highest quality.

If I have an allergy to animals - can I deny STR tenants with service animals due to an allergy?

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

I joked about that but the tenant has pet allergies.