There are ways of coping with cat allergy. It has to do with cat dander. I have a friend whose SO is allergic to cats. My suggestion was to brush the cat regularly, a regular bath

, after a while the cat will get "used" to the regular bath. The bath and grooming helps to control the cat dander. Another thing I suggested was to get a room air filter with HEPA filters to catch the cat dander. We use a vacume cleaner with HEPA filter. It's amazing how much fine dust it collects.
Depending on how severely allergic, and how much are you willing to do, you might be able to live in harmony with the cat. Maybe not...
Just a suggestion.
Sincerely,
smilingcat