Firstly, real policy objectives are rarely articulated to the public. It is perfectly conceivable that there have been many policy objectives deliberately designed to benefit white people at the expense of other demographics.
Secondly, there have been policies deliberately designed to marginalize and assault black communities. One example of such a policy was President Richard Nixon’s ‘War on Drugs’. Nixon’s domestic policy chief John Ehrlichman even admitted as such, saying that “we knew we couldn't make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin and then criminalizing both heavily, we could disrupt those communities." 
Finally, privilege does not always stem from policy. It could be something as simple as seeing your race represented on television, or being able to buy cosmetic products for your skin tone.