Nobody (at least not me) is discounting your allergies (I too am allergic to cats and have asthma) . I believe my question as well as many other posters is how does this affect your flying or when you pass a service animal in the parks? As I have posted elsewhere DH is a pilot at SW and if you are on a plane with a service animal, the service animal and its passenger get priority and you can stay on that flight or they will accommodate you on another flight. If you have a life threatening allergy they MAY ask to see a letter from your doctor.
I used to be allergic to most animals as a child. I had the trio of asthma, allergies and hay fever. As I've gotten older I've fortunately grown out of the worst of the symptoms and tend to get some itching and running nose/eyes now at most. My son has inherited the conditions, which I hope one day he will grow out of too.
So how do we manage. To start with, avoidance is key. Where possible try not to stroke animals, or visit homes with animals. Allergies tend to be worse indoors than out, because of the concentration of allergens. Occasionally well-meaning strangers with dogs have mistaken my sons resistance to go near their dog as fear, actually bringing doggy over to meet DS, claiming that the dog won't hurt him and his name is ... (I on the other hand am terrified. Dogs and spiders...can't stand either).
Sometimes it's not possible to completely avoid though...because of service dogs and real life etc (though I've only ever come across a handful of SDs). We take nasal sprays daily. I find Beconase or Flixonase help to reduce brief exposure to allergens. So if we sat next to a dog owner at the doctors for a few minutes we are generally ok.
For longer exposure (e.g. visiting a property with animals/animal fur or sitting next to a person with an animal for extended periods of time) we have to take antihistamines an hour prior. So, if I'm flying from Washington to Orlando and I notice a doggy in a carrier is coming on our flight, we will pop a pill just incase. Now this makes us feel extremely drowsy - which is great for flying! However, this is not the way I want to fee once I've gotten to WDW! I want to be lucid and energetic enough to enjoy.
Allergies are miserable and whilst it's realistic to think Disney will deep clean every room and there will likely be no issues...what if there was? What if you end up the unlucky person with the reaction. It has the potential to somewhat spoil a very expensive vacation.
I used to find the horses on Main Street MK would sometimes spark my allergy. I remember one occasion I had forgotten my nasal spray and I had to purchase an antihistamine in MK from a gift shop. An hour on I was lying on the pavement in front of the castle, dosing off to sleep. People must have thought I was drunk. It takes a good six hours for the effect of the antihistamines to wear off.
You can buy non-drowsy antihistamines...in my experience they either still make me and DS drowsy or are less effective.
I hope that helps.
Just a note: I have no issue with Disney extending resorts to welcome dogs. I take issue with the timeframe given. They ought to have started it Jan 2019, when people hadn't yet booked and could have made more informed decisions. They should also have considered the resorts, ensuring affordable 5 person accommodation was still available (and not CBR which is a building site).
Because we know Disney Guests always follow the rules, and Disney always enforces. 
