It's my understanding that eating meat for a Jew is optional. We are not commanded to eat meat but if we have the desire we may do so as long as it follows kashrut restrictions. On the other hand, are not Kohens COMMANDED to eat qorban or do they have the option to abstain? In short, can a Kohen be a vegan or vegetarian?
EDIT: Obviously this only pertains to when the Beit Hamikdash existed and/or when it is rebuilt.
The Talmud (Chulin 11b-12a) seems to assume that no one can be a complete vegetarian.
אמר רב אשי אמריתא לשמעתא קמיה דרב כהנא ואמרי לה רב כהנא קמיה דרב שימי ואמר ליה ודלמא היכא דאפשר אפשר היכא דלא אפשר לא אפשר דאי לא תימא הכי לר״מ דחייש למיעוטא הכי נמי דלא אכיל בישרא וכי תימא הכי נמי פסח וקדשים מאי איכא למימר
R. Ashi added: I put forward this argument to R. Kahana — others say: R. Kahana put forward this argument to R. Shimi — and he replied: perhaps the law is that where it is possible to ascertain the facts we must do so; it is only where it is impossible to ascertain the facts that we follow the majority. For if you do not accept this [argument], then the question will be asked: Did R. Meir, who is of the opinion that the minority must be taken into consideration, always abstain from eating meat? And if you reply that this indeed was the case, then it will be asked: What about the meat of the paschal lamb and of other sacrifices?
(Soncino translation, my emphasis)
Yes, but first, some context and reasons why to be a vegetarian.
The Torah prefers vegetarians. In fact, vegetarianism is better for Jewish observances. One does not need to wait six hours after consuming meat for dairy. Only one pair of dishes is required, save for Pesach. One also saves money on kosher meat, which, if you avoid all meat products altogether, you can’t transgress at least twenty mitzvot!
For all the above reasons I think vegetarianism is superior. It also keeps the complexion of the face intact.
Second, the Bible prefers vegetarians (Genesis 2:16). Adam and Eve are only permitted to eat plant food. This changes when humans become cruel and eat meat, resulting in the flood. After the flood, Noah is told that he may consume “Every moving creature that lives will be yours to eat” (Genesis 9:3), with the exception of a live animal (Genesis 9:4; also see Rashi on Genesis 9:3). Noah was "allowed" to eat meat as a concession to human nature. Similarly, Rambam writes that G-d does not want or need sacrifices but "allowed" them as a concession for human needs. Rav Kook wrote that the sacrifices will not continue in the messianic age and that Jews will no longer be carnivores but enjoy plant food.
Since the ideal state for the world is a state when the world will return to the state of the Garden of Edan, an ideal world will sacrifice and meat-eating is barred, it is safe to assume that the Kohen will also be a vegan.
