I would never in a million years re-home my cat simply because I began dating someone who had allergies.
B-A-D advice!!
That is a huge reason why so many animals end up homeless & stuck in shelters.
For the fact that someone else entered the picture + the pets no longer were priorities.
When one adopts a pet, the goal is that the new owner will provide a loving and "fur"-ever home....Not just a home until their pet becomes an inconvenience or a pest, etc.
If someone new came into my life & gave me an ultimatum between him or my cats....Well let's just say that action in itself would showcase to me what an arrogant + selfish person he was!!
Bar none.
When if someone got rid of their cats and later found out their S/O was a liar, cheater or abuser...??!
At least animals are loyal creatures who will ALWAYS offer you their unconditional love for life.