There is an article in the Dining and Wine section of the New York Times entitled "I Love You, But You Love Meat" which discusses the perils of pursuing or maintaining a relationship with someone who doesn't share your dietary inclinations.
Jane and I are fortunate enough to be on the same page that way. It was her idea to go vegan, but I wholly embraced it. I think we'd both been moving in that direction for a while anyway, probably me more than her. Like most people, we put our heads in the sand when it came to thinking about where our food actually came from, but occasionally one of us would have qualms about what we were eating. So we'd been eating more and more vegetarian meals anyway. Our final push into veganism was not animal-related, however. Another member of Jane's family developed cancer, and this scared her enough to want to try a change in our diet.
I can't imagine how you reconcile two completely different eating styles. Sharing food is such an integral part of most relationships. The courtship dance very often revolves around eating out, which could be managed. But what happens when it comes time to start sharing a kitchen? Even if you're not repulsed by the thought of animal product being cooked in your pots and pans, do you really want to go through the trouble of preparing two separate meals, for each and every meal your eating together?
So for all of you singles out there looking for love in all those omnivorous places, below are a few veg*n dating sites. (Caveat: I'm not affiliated with any of these sites, nor have I tried them out, I'm married after all.)
Or, conversely, you can try to get your potential omnivorous mates to read this tongue-in-cheek instructional essay called So You're Dating a Vegan.