Hypernym for "veg" and "non-veg"

I'm not sure why the confusion with the terms veg and non-veg. I live in the northeast US and I hear these terms as well as veggie with some frequency, although it might be because I hang with a vegan/vegetarian/omnivorous crowd where we ask about these things.

I don't have a hypernym specifically for meat-eating, but when I am hosting guests, I ask them if they have dietary restrictions or preferences or, in the case of my kosher/halal friends, strictures. These terms cover the gambit of differences in eating habits, so they would cover your terms as well.

I'm not very clear on your question because "veg" and "non-veg" are not words or phrases we use in English. IF you're referring to someone who does not eat meat, that is a vegetarian.

It is reasonable to ask "Are you a vegetarian?" or "Do you eat meat?" A more general way to ask is "Do you have any dietary restrictions?" or "Is there anything you don't eat?" There is no real conversational opposite to vegetarian, so we'd just say "I'm not a vegetarian."