==Non-hispanic whites + blacks made up 95% of the population as recently as 1970==
The large immigrant communities from Italy, Germany and Ireland were not considered "white" when they first came to the US. Only later did that occur as definitions of race have changed over time, usually to serve a political purpose.
==the fact that the U.S. has gone from one (black Americans) to two (added Latin American immigrants — now 16% of the population) racially delineated underclasses does a lot to undermine social cohesion.==
Have you explored the possibility that people's obsession with this is what has actually undermined social cohesion? It has happened before in American history with the Know-Nothing Party.
==Source for U.S. demographics==
Your own source shows "whites" (72.4%) and "blacks" (12.6%) as making up 85% of the population as of 2010. You have decided to further delineate that into "non-hispanic white" which is not an actual race. Also notable that you don't split out the differences of Southern Italians and Northern Irish. Do immigrants from Spain count as white or Hispanic?