Not sure I understand your point.
MLK argued that modern society needed to integrate. He saw that separatism inevitably contributed to discrimination.
Sociologists have argued that humans naturally form social groups to compete for dominance. The key word is dominance... not equality or equity. So, unless you can breakdown identity politics which is a fancy word for "tribalism", you are always going to have conflict.
And so, the only way a "nation of immigrants" can avoid internal conflict, apartheid, and violence is to move towards an integrated society where people identify as "one nation, one people".
My family is an example of MLK's dream. One of my parents was German and the other mixed German/Carribean. I married twice. My first wife was American born with a diversity of European ethnicities. My current wife and I have been together 36 years. She is Chinese from Indonesia.
So, my children are white and mixed white/Chinese. My oldest child married a woman from Africa and has four children. All but one identifies as mixed race American, the one identifies as "Shona American". So should Shona Americans have their own quota when looking at diversity?
Like Europeans, Africans don't identify as African, but rather based on their ethnicity. When I grew up no one identified as "white"... German, Slav, Polish, Jew, Italian, French, Spanish... yes. White... no. Looks like that phase of mixing is going smoothly for the most part.
My oldest daughter married a Nigerian, they divorced, and she had a child with her partner from Haiti, who is 25% Hispanic.
My youngest two children no matter who they marry, if they have children will have Asian/white and whatever their spouses background is.
You seem to presume American culture is white culture. But it's not.
My German cousins don't eat, dress, or even listen to similar music as I do. They don't celebrate the same holidays; they don't study the same history. American culture is American culture, and our history is for all Americans. I celebrate MLK day, Thanksgiving, Presidents' Day, and the 4th of July, my European cousins don't, nor should they... they aren't Americans.
Last week, I drove to a nearby city to buy Nigerian food. Earlier that week, I bought Brazilian food. During the week, my wife prepared good old American barbecue ribs with Asian spices. I also enjoyed some Hawaiian poke from Costco.
In simple terms, America was designed to be a melting pot, not a rainbow of distinct cultures or the turning everyone "white". When you mix yellow and blue, you don't get yellow or blue, you get green. The mixing bowl can't stay yellow and blue, it has to turn green, the only question is how long it takes before it turns green.
That is how culture, race and traditions work. My wife prefers "real" Asian food, my children prefer Asian fusion food. My African daughter-in-law occasionally cooks some "real" food from Africa. African American food is like Asian fusion food, it has its roots in American and African cooking.
There really is no "black" culture. My African daughter-in-law had nothing in common with my Nigerian son-in-law or the father of my Haitian American granddaughter or my African American friends. Each of those cultures are distinct, the only thing they share is skin color and even that varies enormously from deep brown to barely brown.
Your individual choices including what traditions you celebrate, food you consume, clothes you where are your personal choices and I fully support that. But separatism is different.
Separatism argues that if you are black, you should marry black, dress black, talk black, vote black, etc. Separatism tries to shape the way you think into that of a black person, not an American with black skin.
MLK's dream of an integrated society will happen as long as we teach our children to embrace each other as individuals and tolerate individual differences rather than teach our children they belong to an identity group and disparage other groups. In other words, I support diversity at the individual level... if a white person wants to embrace African culture, tradition, food, and clothing... go for it. It's okay. If a black person wants to eat bratwurst with sauerkraut, enjoy.
Don't tell people what they need to think or how they have to behave based on their skin color. A black friend who I love but ideologically disagree with on identity argued the other day, that any black conservative is an "Uncle Tom" for betraying his race. In his view, it is okay for white people to be conservative but not a black person. This concept of racial conformity highlights the tribalistic nature of separatism.