Was it capitalism or was it refrigeration?

In some circumstances you’re absolutely right. In many parts of the word, meat was either scarce or difficult to preserve. In other parts of the word, some peoples survived almost exclusively on animal products. The natives on Alaska are the first that come to mind.

Of course “meat” was a very important part of their diet, they relied heavily on organ meats for their essential vitamins and nutrients. They were significantly more humane and less wasteful than we are today.

That's sorta half the story. The official statement is that consistently eating more than 1.5lbs (500g) of red meat per week "probably" (their word) increases your cancer risk. The real story is that eating more than 50g of processed meat per week dramatically increases your cancer risk. To the extent that processed meat is ranked as a "Group 1" carcinogen.

Flip-side, grains and legumes have been tied to cancer as well. I can't find exactly what category, but they seem fairly convinced they are carcinogenic.

It is, sadly, like the California Cancer joke, where almost everything causes cancer if taken to excess.

The dose is the poison. Meat in the amount we consume today is unhealthy. In the past people didn't eat meat every day or even close to it.

Everything in moderation

This is a common explanation but is unfortunately propaganda in itself.

https://rationalwiki.org/wiki/Weston_A._Price_Foundation

Long story short on what you wrote - meat is a nutritionally rich food option and kind of nutritionally acceptable if your people have been living in the tundra for a few thousand years & have actually managed to genetically accommodate it, since there isn't much else food the further you go north (although it's very much overly simplistic to depict Inuit diets as entirely meat-based). But for modern people, in temperature or tropical regions, it makes no sense at all, plant-based diets give you the best balance of nutrients without extremely high fat and cholesterol content...there's a real anti-scientific hubris going on with people trying to brush away this basic fact.