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There is the story of Maharishi Agatsya digesting the demon Vatapi after eating him. Vatapi could assume any form he chose. He also had a boon that even if dead he would come back to life if someone called out to him. So he and his brother hatched a plan to eliminate all Brahmins. Whenever any Brahmin or rishi passed their land, they would cordially welcome them. Vatapi would assume the form of a goat and he would killed, his flesh cooked and fed to the Brahmins.Thereafter his brother would call out "Vatapi where are you. come here. Vatapi would come out tearing the stomachs of the people.

Many of our scripture are the inverse of rationality, especially in today's time. Respecting this sites rules, I will refer the text from Bhagavad Gita (BG), which I feel still relevant to this date (not saying that it's the only relevant text). I would refer links from Vedabase website, but it's recommended to understand Sanskrit or read other similar sources as there are some mistranslation in their English.

Brahmin

First, we need to be on the same level of the definition of "Brahmin". The 4 sections of society are created by lord:
BG 4.13

According to the three modes of material nature & the work associated with them, the four divisions of human society are created by Me. And although I am the creator of this system, you should know that I am yet the wonder, being unchangeable.

Brahmin > Kshatriya > Vaishya > Shudra
divisions are based on their nature & work. "Nature" is derived from an arbitrary combination of Satva + Rajas + Tamas and "Work" is derived from one's Karma.
So leave behind the mooted notion that the division system is based on surnames/caste/family. After that, you would be able to accept the divisional superiority (as indicated above) without any controversy!

In today's time, we can over-simplistically divide the people as below based on Karma:

1. Brahmin: Seekers.==> scientists, teachers, spirituals, philosophers
2. Kshatriya: Warriors.==> army, police/security, politicians, sportsmen
3. Vaishya: Traders.==> businessmen, merchants, artists
4. Shudra: Workers.==> social servers, all jobs in various fields

One might have a genuine doubt, ultimately teacher/scientist is also employed, then is he Brahmin or Shudra? A politician makes so much money, is he Kshatriya or Vaishya.
So here comes the division based on Nature:

1. Brahmin: works for Enlightenment of self/society
2. Kshatriya: works for Pride of self/society
3. Vaishya: works for Fulfilment of self/society
4. Shudra: works for Service of self/society

All the 4 divisions are respectable and required for any society to run. This is how, you can divide the whole world into 4 sections irrespective of religion. e.g. Dr APJ Abdul Kalam being a Muslim is more Brahmin than Mangal Pandey (born in Brahmin family) who was in British military and fought later against it in 1857.

Today, we are living in a hybrid society which was worried by Arjuna and Krishna both during the discourse of Gita.

Non-vegetarian food

Looking at how a Brahmin would behave like, do you feel he needs to eat non-vegetarian?
A person who is a seeker of truth & knowledge and who works for enlightenment would not care for the fulfilment of taste buds and level of bank balance. There is nothing wrong if he does, but then he is more of a Vaishya than a Brahmin.

Counter questions:
Forget scriptures. What if the question of survival?
Yes, in such case it can be appropriate to consume meat. But remember, that it should be really for survival, as good as Eskimos! A very famous event of 1972 Andes flight distaster, where some of the passengers survived based on dead human flesh in Icy mountains. People looked at them with disgust at first, but then they were accepted.

Forget survival. How about nutrition?
There are so many superior veg options easily available for protein, e.g. Soya-bean, Tofu, Paneer(Indian Cheese), Chheno (milk product), Broccoli. They are better in many health and nutrition aspects compared to chicken/mutton/beef/fish.

Forget nutrition. What's wrong with fulfilment of taste-buds?
It's quite expensive for others. When you eat non-veg, virtually imagine that 3 hungry kids somewhere in India/Africa looking at you with merciful eyes. The amount of land required for animal farming is 4 times than the cultivation of vegetable plants.
Also think about: animal cruelty, CO2 emission, greenhouse effect, health risks

Conclusion

Not appropriate to consume non-veg food in general especially in today's time when options are so vast.

Those we call demigods in our scriptures are the embodiment of various nature elements like water, wind, earth, fire and so on. Today nature's cycle is highly disturbed due to human intervention. That's equivalent to betraying those demigods.
If we snatch away the animals/vegetation from nature, but cannot repay its debt back then, Lord Krishna has called such people as Thieves, be it for veg or non-veg.

BG 3.11

The demigods, being pleased by sacrifices, will also please you, and thus, by cooperation between men and demigods, prosperity will reign for all.

BG 3.12

In charge of the various necessities of life, the demigods, being satisfied by the performance of yajña [sacrifice], will supply all necessities to you. But he who enjoys such gifts without offering them to the demigods in return is certainly a thief.

BG 3.13

The devotees of the Lord are released from all kinds of sins because they eat food which is offered first for sacrifice. Others, who prepare food for personal sense enjoyment, verily eat only sin.

Hope this Helps