I like someone and I'm 70% sure she's interested in me too.

Things seem fine and all to let the potential relationship grow, but then I realized we're opposites when it comes to our dietary preferences. I'm a meat eater and I enjoy grilling stuff frequently. In fact, I generally don't give a shit where food comes from, as long as it's tasty. She, on the other hand, fancies herself as a vegetarian and environmentalist(she eats seafood sometimes though). No meats at all, and even acts a bit self-righteous about "sticking it to the meat industry" by not eating or buying anything meats. She's no PETArd though, and says her diet choice is primarily to live healthy.

So I ask you all, do people who have contrasting diets have any hope of a stable relationship?

Indeed people do. I'm friends with a hard core vegan whose husband eats cows by the slab. She cooks vegan style food, and he rejects it and cooks for himself. He's actually a bit of an ass about it, teasing her sometimes about her lifestyle choice (they married before she went veggie), but at his core he's supportive of her and does occasionally eat what she prepares. It is a bit more expensive to have to buy groceries that support two very different diets, but it works for them. It's all in one's mood. If she cooks vegan, keep an open mind and try it out. She won't partake of your beef fest, but I should assume your consumption habits won't turn her cold.

Just be open and prepared to bend every once in a while. Might be a pain at first, buy you may very well adjust.

In the early stages of dating, I don't think this will matter too much. If you initially go out to restaurants you can order different things. If you really want to become closer though, you'll have to find a middle ground.

I bet both of you could learn a lot just by researching health and diet information. Vegetarians encounter a lot of problems with their lifestyle (humans are built to be omnivores) but over-consumption of meat is bad for you too.