When did we make our biggest gains in reducing racism in America? I think people would point to the 40's-60's. The military, sports, and entertainment became integrated. Voting and some property and access rights were greatly improved. There have been improvements since then, but more gradual - no more big splashy stuff, and I think that is part of the frustration.
It is at least co-incident with the period when we had much less immigration, 1927-1964. The common declaration is that all prejudices go together, and reducing prejudice against immigrants is just the same thing as reducing it against blacks, with the requisite accusations of white American disliking "brownness" in general. That's a favorite formulation of Barack Obama.
What if it's just not true? What if it would be better and more praiseworthy if human nature were that way, especially in aspirational, open-hearted America - but it's just not? That black soldiers fought as Americans in WWII and Korea and acquitted themselves admirably was referenced repeatedly in the 40's -50's for integrating one area after another. Harry Truman mentioned it specifically when he integrated the armed forces, that it was a shame to do otherwise. It was a big selling point in integrating baseball.
Maybe as a practical matter no people expands their definition of "us" very easily and citizenist is the way to go. We sometimes speak of immigrants making it harder for blacks to get ahead in terms of employment and wages - it was one of Bernie Sanders's core values until he gave all those away. We aren't supposed to mention that, but it is likely true for economic gain. What if it is also true in an emotional, associational sense? What if Universal Brotherhood is actually a dead end, and step-by-step changes of becoming a people are all that is possible?
I don't know this to be true. I simply note that it is possibly true but no one says it. Which in turn immediately leads to "Why don't we want this to be true? Why is it not one of the cliches of the discussion, rather than an unmentionable?" There are plenty of untrue cliches out there all over the political spectrum, but this one is not even a Facebook poster.