While the civil rights movement was largely "peaceful" (loaded word with little meaning), it was also incredibly disruptive. People in the movement were very rude to moderates who advocated in favor of negative peace while reaffirming their appreciation of the status-quo.

MLK's position here was not that the people within the civil rights movement needed to be more respectful to white moderates. His position was that the moderates were the issue. The people who consistently advocated for negative peace were the issue.

The leaders of vegan movements also don't generally go around attacking the moderates of our time who appreciate the status-quo and advocate for negative peace. There are individuals that do attack moderates, just like there were individuals in the civil rights movement who literally physically assaulted white moderates (much worse than calling someone a cheese-breather and having their feelings get a bit hurt). Again, MLK did not draw attention to these fringe cases because the actual issue were the moderates themselves. Some might even say the racists deserved to be beaten, and that's not even something I would necessarily argue against.

Veganism is the same. The issue is not the people who are a bit rude online to bloodmouths/carnists. The issue is the moderates themselves, their constant advocacy for negative peace in place of positive peace needs to be shut down unequivocally.