At the height of the American civil rights movement, when theories of oppression might be expected to have some resonance, privilege politics were virtually unknown. The privilege model was unable to find a foothold among the hundreds of thousands of anti-racists involved in the country's massive and often integrated struggles for freedom. Only later, during the tragic crisis and disintegration of the New Left at the end of the '60s, were privilege politics able to gain a hearing--among white, middle-class students, most of whom had had no involvement in the civil rights novement. White-skin privilege theory would come to play a major role in the destruction of Students for a Democratic Society  (SDS) by extreme sectarians.Now, while this short article may accurately explain how Privilege Theory became popular in parts of the communist left, it doesn't explain its general history. Derrick Bell, the father of Critical Race Theory, was a black man who took part in the civil rights struggle but, unlike Martin Luther King and Malcolm X, had no interest in socialism. The appeal of privilege theory isn't to whiteness—it's to middle-classness, because it does not challenge the privilege of the rich. Privilege theory only insists that the exploiters should look like the exploited.
ETA: From a response to the article, Tarred with the same brush | SocialistWorker.org:
It is quite clear that privilege theory became something else in the 1970s and '80s. The writings of J. Sakai of the Maoist Internationalist Movement are, to this reader, the clearest exposition of a theory where white workers are just not part of the revolutionary subject, and are considered instead as active beneficiaries of the system. This is a dangerous, demobilizing theory, and the ISO is correct in fighting it. But I certainly think it is unfair to tar Ted Allen with the same brush.