If whites were truly privileged, he wouldn't have pretended to be black. (We can discuss the weird standard that if he said he identified as a woman that'd be allowed separately.)
But he's pushed for the most virulent racism against whites in order to prove his bonafides as a black man. And that vicious vein of hatred is evident in the leadership and statements of general BLM members, which is why Shaun King as well as everyone else in the group is partially responsible for the attacks on cops from Dallas to Baton Rouge to the BLM member who broke into a cop's home to assault him before being shot (but reported as home breakin, not BLM incident, since he didn't kill that cop).
Black Activists Call for Lynching and Hanging of White People and Cops
Caught on Video=> Black Lives Matter Leader Calls for Running Over, Shooting Police
BLM activist advocates white genocide at Harvard
NY BLM Protesters chant, “What do we want? Dead Cops.”