Robert Kennedy was too optimistic about the coming "civil rights revolution". This is due to the fact that even if we abolish poll taxes and segregated areas and murder of unfortunate blacks/Mexicans/Chinese/whatever, internal opinions are still always biased against blacks. Research done by the Implicit Harvard Project shows that most people are biased toward blacks subconsciously (or non-subconsciously) and that people still don't want to be around black people in general. 80 out of 100 white people say that they do not want to be around people of different race, and 70 out of 100 white people don't want their kids to be around even the best behaved blacks, saying they're "bad influences." Many people just don't enjoy being with Negroes:(
You reference a study (I believe the Implicit Association Test (IAT) that found white and biracial people tend to favor white people and tend to associate more good with white people. A big problem with using this test to correlate some implicit degree of bigotry into the general population is that the question of why this bigotry exists is not answered. Is it inherent or inherited from our culture? You need to provide causation to substantially link the study in support for your prediction.
Humanity has a great deal of evolutionary baggage that it's learned to cope with and compartmentalize. Human history indicates we are moving in towards a more fair world. Note the way we have changed on slavery, women, LGBT, all in just a century.
Wow, you've done your research! In the South, many children are taught that blacks are inferior BECAUSE they are black. Sometimes the teachers reference studies that blacks aren't as smart as whites (such as Performance Series, COGAT, etc.), but most of the time teachers just teach that blacks are worse than whites. And this is NOW, not the 1960s!
Another thing is that almost everyone in the US has a biased opinion of black people (even some blacks!) Research shows that most parents unintentionally teach their children to have biased opinions of black people. Why? Because the parents are biased toward blacks. Our government may have forced our outside to change and allow black people to get jobs and all that, but we still are all biased.