Almost every veggie forum has a thread on this. Should I date a non-veg, can you date a non-veg? I'm going to throw you hopes of getting an answer out of the window here. I don't know. Here is how it works for us though.
We're both quite laid back people in our own way. We don't really stress about our differences and it doesn't bother us that we eat different things.
Stephen has stopped eating red meat since he met me but I never tried to persuade him too and I don't try to persuade him to give up more. He - of course - has never tried to make me eat meat.
When tea time rolls round you can usually find us cooking and eating separate things. Sometimes it's completely separate. Stephen has a list of food he doesn't like so when I'm craving curry or Chinese food I leave him out of it.
Occasionally we'll try to eat the same side dish and different mains. Here I've made myself an extra large portion of Home Fries with added mushrooms and a large dollop of salsa. Stephen's fries got put into a separate pan when I added the other veggies to mine as he isn't a fan of peppers or onions. His is served with breaded chicken.
Other times we manage to eat the same thing. He wants to experiment with spinach so we made potato and spinach gnocchi, served with a dollop of cheese sauce. It gave us a rare oppertunity to cook together and made us feel warm inside.
I know this isn't an exciting post but we're not the conflict type. But this is how our kitchen works. And if you are trying a mixed relationship, good luck.