Q:

Galactics look like food animals

This unidentified story was described in Jeff Dege's comment on the question "Fantasy story circa 60s about a sheltered vegetarian boy who visits a slaughter house with dire results":

Earth makes contact with a galactic civilization. Which reacts in horror when they find out that domestic turkey looks exactly like alien-race-1, which is a long established and well-regarded member of the galactic alliance.
Earth agrees to no longer eat turkeys, when it is discovered that cows look exactly like alien-race-2, and the chickens, and pigs, and fish, etc.
Eventually, humans decide that they'll need to be vegetarian, "but at least we can still eat yogurt", to which the galactics react in horror, explaining that alien-race-X is a form of sentient bacillus culture, and that the idea of eating something so very like them is anathema.
At which point Earth withdraws from negotiation, and passes a law decreeing that everyone has the right to eat whatever he damned well pleases.

What story is this?

A:

"Flat Tiger", a short story by Gordon R. Dickson; first published in Galaxy Science Fiction, March 1956, available at the Internet Archive.

"I am in no sense an official, but I could hardly wait to offer you the tentacle of friendship on behalf of the Galactic Confraternity of Intelligences."
[. . . .]
"Eaters of what?" said the President of France.
"Energy. My dear sirs," said Captain Bligh. "You surely would not wish to continue with your present diets. How could you eat anything you love? And love, like charity, begins at home. Moreover—" he went on—"how could you expect the rest of the Universe to accept you otherwise? Consider the similarity of shapes. For example, what a Red-eyed Inchos would think on arriving to set up a modern weather control system for your planet. If he should see one of you sitting down to—" the Captain shuddered—"a roast turkey, except for a slight difference in size, the exact image of himself. Similarly with a Lullar and a barbecued pig, or a Brvandig and a baked sturgeon."
After a moment, the President of the United States cleared his throat.
"Perhaps—" he suggested, "a strictly vegetarian—"
"Mr. President," said Bligh, interrupting with dignity, "I am myself only one of uncounted myriads, but some of my best friends are plants." I hate to think what a Snurlop would say if he happened to see a loaf of your bread and imagined a child of his own being harvested, threshed, ground and even baked!"
"But now—" interposed the President of France hastily "certain liquids such as wine—"
"Please!" choked Bligh, turning green. He staggered and leaned against the desk beside him. Hastily the President of the United States fanned the Captain's face with a major-general's appointment that happened to be lying close at hand. Slowly, the color returned to Bligh's face.
"Please," he repeated feebly, "amputation, crushing, fermentation—horrible." He shook his head. "No—no liquids."
"Water," said the Prime Minister.
Bligh looked at him. "Think," he said, "just think of the minute organisms that must die, either through being boiled alive, poisoned with chlorine, or digested living, to provide you with ordinary drinking water. Why, the Fellibriks of—"
[. . . .]
So that is how peace has come to the world. We are united at last as we have never before been in history, united as one people behind what has come to be known as the UnBligh Doctrine, and which is now emblazoned in letters of gold over the front doors of the U.N. Building.
No government or individual or collection of individuals shall have the power at any time to come between any other individual and the due and lawful exercise of his appetite.
Let the Galactic Confederation of Races beware!

Arrogant Worms — "Carrot Juice Is Murder"

