here's an article:
10 ways white people are more racist than they realize, though you may disagree with the claimed facts...
basically it's interwoven into the fabric of society and racist attitudes are passed from parents to children (largely indirectly i'd imagine). media probably reflects it quite keenly, and so we can absorb racist attitudes that way too. i guess i personally would look at it as a problem of culture, so if there was something i thought the government could do it would be to somehow facilitate dialogue in communities about it (ofc it would be up to people to participate). i really think it is a problem that most whites (myself included) don't feel comfortable talking about it and avoid the entire subject, because that suggests basically freezing any progress. meanwhile all the racist attitudes continue to recycle through culture. basically people need to change their attitudes and need to be able to talk to those with different cultural backgrounds in order to come to understand something beyond "people like me." anyway i'm not sure what the best way to "facilitate this" would be, and it seems when the govt goes forth on any project (education, health care, the eternal war in the middle east, etc.) it turns out to be an expensive and utter failure. and this one would probably not be an exception.
(by "facilitate" i mean in a non-creepy way, like not a weird government club that forms in all the major cities with a terrible sounding name that brainwashes you with the "right" govt-approved way of thinking while strongly encouraging everyone to smile and hold hands)
another thing i would add is that not only is race a "cultural construct" but it is one that is consistently used to keep power away from certain "others." the concept is used to define differences between people, so you can carve out a section of the population (linked through culture and/or ethnicity), assign them a label, and deny them equal footing. to define a 'race' is already racist.
anyway the point about slavery is that thought constructions in the minds of the people back then are still here because they've been passed to children and grandchildren and so on.