King wouldn't have been onboard with the white privilege concept. He rightfully believed it wasn't a color privilege, but a financial class privilege. In King's earlier years it was absolutely a color issue because even a well-to-do negro would face the same restrictions as poor one, but the government's role in using poor folks to go die for the liberty of another country when they haven't found the same in their own, or the concept of fighting and dying side by side but not being able to live in the same neighborhoods or go to the same schools at home, that was the issue. It wasn't about internal prejudices, but government ones.
The left has since made it about personal prejudice, and they've morphed ins utionalized racism to just any discrimination for any reason.