Many people may be allergic to a species of animal (dog, cat, bird) but have no reaction to the family pet.
The allergy is to the animal saliva
, and not to the fur or dander. By being constantly exposed to the unique saliva of that particular animal the allergic response is diminished - their immune system no longer reacts to that one. However other animals will still cause an allergic reaction
Answer assisted by Ken Starnes, Medical Student