I don't know the right answer for you, OP, but in my family we are all allergic to pet hair/dander (and I break out in a rash if a horse slobbers on me, fortunately I can avoid this in day to day life!) and we all have had cats all our lives, wouldn't be without them.
One sister has asthma which she manages with inhalers. She sometimes takes antihistamines for allergies too.
One sister takes loads of antihistamines, she is the most affected by allergies. She also has dogs and horses in addition to cats!
I just sneeze and snuffle periodically and don't think much about it. Dust and pollen and other things are also making me sneeze and snuffle too. It's just not a big deal.
None of us have had our health significantly affected by this, it's a minor irritation to us which doesn't outweigh the love and companionship we get from our pets.
Your H, like many others on this thread, may be more severely allergic and it's a serious concern to him. Or he may only have minor symptoms, but prefers not to experience them, and that's his choice.
Just wanted to give the perspective of someone who suffers from mild symptoms but will ignore them for the sake of the bloody cats ;-)