A lot of the things I enjoy doing with my partner involve food. We go to street food nights and restaurants very often, and we cook together a lot. Of course our tastes aren't exactly the same (for example, he loves spicy food and I just can't handle it). But generally, we like roughly the same things, and a lot of that is meat. Meat is a huge part of my diet. If I dated a vegetarian, about 90% of the things I like to eat and 90% the food-related activities I like to do would be off-limits.
So no, I wouldn't date a vegetarian or vegan, but not out of some kind of moral disagreement, but simply a case of inconvenience and not being able to eat together.