My issues with it:
1) Kissing someone who's just eaten a burger/loads of cheese would really put me off - I'd feel like I was eating it myself.
2) I don't think I could be in a long-term relationship with someone who had really different principles to me. For example, I couldn't date a religious fundamentalist, a right-wing extremist, someone pro-war or a homophobe, because we'd agree on virtually nothing. The same is likely to be true of an omnivore, unless they were very understanding and agreed with my principles, even if they couldn't bring themselves to give up meat.
I'd be much more likely to date a lacto-ovo-veggie than an omnivore, although if they ate loooooads of cheese I'd just find it gross, coz cheese makes me want to vomit.