It would certainly be great to date another veggie, but I wouldn't refuse to see someone just because they weren't.
All I ask is that an omni that I date be respectful of my veganism and not try to kiss me with meaty mouth. I wouldn't kiss a smoker unless he/she brushed his/her teeth first, so I guess I'd handle meat the same way.
If I got serious with an omni to the point of living together or being married, then we'd have to sit down and talk about compromises ahead of time, such as not having bloody hunks of meat dripping onto my veg food. Separate refrigerators would be ideal, I think. All of my veggie food, and all of my partner's non meaty omni food (I'm willing to compromise on dairy products being in the 'fridge since they aren't really gross to look at as long as they are packaged) could go in the main 'fridge, and a little small mini-fridge like you'd use in a dorm room could hold the SO's meaty stuff. I could handle frozen meat stuff being in the freezer if it was in something...like if my partner wanted to keep some frozen pepperoni pizzas or whatever in the freezer, but I'd be uncomfortable with big frozen slabs of flesh being in there.
I think that's reasonable.
And I think I've gone off on a tangent, heh.
I live with omnis right now, and it's never fun to open the 'fridge and see a big bloody hunk of meat marinating or something, but I cope because I know it's only temporary while I live with my family and save up for a house of my own.
The idea of living the rest of my life with the prospect of facing big bloody hunks of meat in the 'fridge is a little harder to cope with, I think.
But to get back to the strictly dating thing...unfortuately, it does appear that there are more veggie women than men, which can make it harder for veggie women to find male veggie mates. I happen to be willing and able to date both genders, but that's just my own personal sexuality. Heterosexual veggie women probably have a harder time.
I try to remember that most of us were omnis once (I certainly was) and it took someone showing me how wonderful veg*ism is to really open my eyes and make me curious about it. (Side note: I later learned that that person was actually a pescetarian, heh. But she made me curious enough to investigate veg*ism, and the research I did is what really converted me.) Maybe an omni person that I date will have a similar experience. But I won't try to forcibly convert anyone or anything.
So yeah, I think I've rambled enough. ^^;;
ETA: I should clarify, I'm willing and able to date both genders if I'm free to date whomever I want. I just started dating someone recently, though, so I'm not in the market at the moment, heh. (I didn't want to give a false impression. Gosh, this is wordy. Sorry.)
We see the world as "we" are, not as "it" is; because it is the "I" behind the "eye" that does the seeing.