Does Bhagavad Gita say anything about whether a person should eat Vegetarian or Non Vegetarian food?
Here's the most specific dietary "guidelines" I could find in Śrīmad Bhagavad Gītā,
BG 17.8: Those foods which promote longevity, strength, health, happiness, and satisfaction;
Which are juicy, oleaginous, nourishing, and pleasing to the stomach, are dear to those flourishing in sāttva (bright righteousness).
BG 17.9 Those foods which are bitter, sour, salty, very hot, pungent, dry, and overly-piquant;
Which produce pain, grief, and sickness, are dear to those caught in rajas (passion).
BG 17.10 Those foods which are stale, bland, putrid, and toxic;
Which is ort or unfit for sacrifice, are dear do those drowning in tamas (dark destruction).
So, we can dissect this to get a little more clarity on specific foods.
- tamas foods: Foods unfit for sacrifice include donkeys and camels as well as anything which is expiring. Ort are the scraps left over from preparing the meal: the chopped-off ends of vegetables, certain peels & skins, etc. Toxic foods are anything that harm the body. As for stale and bland foods, I believe this includes many meats because we don't like to eat them without first spicing them up.
- rajas foods: I think these are pretty clear. You can tell if something is too bitter, too sour, too salty, too hot in temperature, too pungent, dry-tasting, or too piquant ("spicy" like chilies). If you end up on the toilet after a meal, something was rajas. Personally, I consider pork to be rajas because, if I eat it after a prolonged absence from eating it, I feel very nauseated.
- sāttva foods: Juicy foods include most fresh fruits and many fresh vegetables. Oleaginous foods are often pressed for their oils. This includes most nuts & seeds as well as some other things like olives.
Of course this is no definitive list, but it's hard to be very precise without delving into interpretation. Other than the above, the only other mention of foods in the Bhagavad Gītā is in reference to ceremonial sacrifice or the below quotes.
BG 6.16: Yoga is not eating too much, nor is it not eating at all;
neither is it sleeping too much, nor not sleeping enough, Arjuna.
BG 3.13: The saintly, who eat what remains of the sacrifice, are released from erring;
but the erring, who cook only for their own sake, consume their own impurity.
BG 9.27: Whatever you do, whatever you eat, whatever you sacrifice, whatever you gift to others;
and whatever austerities you undertake, Son of Kunti, all that you offer to Me.
So, keeping in mind BG 17.8~10, I think you can discover for yourself which things are fit for eating, and which aren't. Just don't forget BG 9.27 & 3.13; when you eat, remind yourself that it is a sacrifice to God within you. And also per BG 6.16, eat in moderation.
Note: “The question: Does Bhagavad Gita say anything about whether a person should eat Vegetarian or Non Vegetarian food?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.