My mother was the same way. She'd always said she'd kill a cat if one came in the yard, but we had wild barn cat when I was little and she never did anything with them and when my lab brought home a kitten from somewhere, he moved in and she's all about him, though she still likes to talk mean about him, she's always checking on him and making sure he's got what he needs.
From what you've said, your fiancé is the same way. I think he'd like one, once he got one. One option you have is to foster. You'll want to pick one that is real laid back and doesn't have any behavioral issues, like spraying or clawing. You don't want to try to sell him on the idea of a cat with a misbehaved one. This would let him see what it's like to have one without the commitment.
You'll also have to decide what you're willing to live with and compromise on in your relationship. You've already made a big commitment to be together by buying a house, but having had animals all my life I understand where you are coming from and not having animals around would be a deal breaker for me. You can't count on him to change and you'll have to decided whether it means enough for you to push the issue and what you'll do if he still says no. When it comes down to it, you're equal in the relationship an your "Yes, kitten" is equally as valid as his "No, kitten".
However, I don't think it'll really come down to that. Tell him if he wants a "real pet" he can get a dog, but I have both and the cat frequently abuses and beats the "real pets". He also loves to snuggle, is okay with doing his on thing when you don't want to, is low maintenance, and goes out to use the bathroom, so there isn't even a litter box to clean. I think he'll get attached fairly quickly. Good luck, meow.