What do you do if you're a cat lover and your S.O. is a dog lover?

I’m not currently in this situation, but I very well may be in the future.
I cannot stand dogs. I’ve had a horrible history with them (a couple of traumatic incidents, I need not say more).

So I’m all about cats. I can’t imagine a home for myself without a pet cat. But I’m worried that I’ll meet a wonderful man who’s perfect in every way…but loves dogs (and hates cats).

What would you do? Which person would have to sacrifice for the other?

(Don’t just say “get a fish.” Fish can’t cuddle.)