When people state to be allergic to cat hair, it is not in fact the hair itself they are allergic to. But it is a certain protein in the cat’s saliva, or cat dander that gets transferred to its fur when it grooms itself that causes an adverse reaction in some people.
When the saliva dries, it becomes airborne and this protein is 1/3 the weight of regular house dust and therefore, can travel far and wide, even to places where there aren’t any cats. Bathing the cat regularly with warm water should be the solution to make its fur more endurable to an allergic person.