MLK actually alienated white moderates to about the same degree that vegans alienate carnists. It was only retroactively, after the civil rights movement, that white moderates pretended like they were aligned with him all along. In 1966 MLK was polling in the low 30s among white Americans.

I'm sure future moderates/apoliticals will do the same with veganism. Lab grown meat will become a thing, we'll outlaw our barbaric practices of animal torture and slaughter, and those future generations will look back with horror at how savage we were, and all the moderates will proclaim proudly that "I would've been a vegan if I was born in the late 20th/early 21st century", and they would be almost always wrong.

It's similar to everyone's modern position on slavery. If you polled the majority of the population "would you be an abolitionist if you were born in the early/mid 19th century?", you'll get the vast majority of people saying they would've been, but the vast majority of people were not, and its not like we had some evil gene in us that got naturally selected out of us. People were just normalized in that environment. People today are just generally incorrect about what the impact of normalization would've been on them in the past (or even what the impact of it is on them today).

The people in Washington listened to MLK because he was radicalising hundreds of thousands of people, and if his demands were not met, the politicians worried that those people would start listening to Malcolm X. The radical and moderate sides of any movement exist in symbiosis. They are the carrot and the stick, working together. The owning class likes the carrot much better than the stick, so they give credit to the carrot. But you need radicals so that you can say "look who's coming for you if you don't listen to me". It's good cop bad cop.