I was very much allergic to cats as well as dogs and other animals as a child. My dog allergy was fairly mild, and after I graduated college I got a dog for a companion. The dog bothered my allergies a bit at first, but after a while the allergic symptoms vanished completely. I’ve owned dogs pretty much continuously ever since then and have never had allergy problems with them.
Cats still bothered me though.
Many years later, my wife got a cat for our son, without talking to me about it first. The cat bothered my allergies at first, but again, after having it around for a while the symptoms abated somewhat. They didn’t vanish completely like they did for dogs. Then we got more cats, and now we have four.
It used to be that I would have an allergic reaction just going into a house that had cats in it. Now I can go anywhere around my house and I don’t have any kind of reaction at all. If one of the cats sits in my lap and i pet it, I will have an allergic reaction (itchy eyes and a stuffed up nose). One of the cats bothers me more than the other three for some reason. One of the other cats sleeps with me often and doesn’t bother me at all.
YMMV of course, but that’s my experience.
I had itchy/watery eyes and a stuffy nose around cats as a child. I never had any kind of asthmatic response.