As an Afrikaner myself I can report that there still is a great deal of white privilege here, though it really flows simply from economic power rather than law or race as such. I.e. it is more a generalized rich privilege, shared by the black upper middle class.
Anyhow, it is a mistake to think the ANC opposes this. Since the end of apartheid, on average, white people have become even richer than they were before, and the gap between rich white and black poor has actually widened. And all of this happened as a direct and quite predictable result of the ANC government’s policies. Thus, one must assume that the ANC wants this to be the case.
The white population is the goose that lays the golden taxation eggs, and they also constitute a convenient scapegoat for everything that goes wrong. In the meantime, a black population increasingly dependent on government welfare will continue to vote for the ruling party out of fear that they might otherwise lose their welfare.
Last but not least, the ANC-induced utter collapse of government services has created a huge gap in the market for entrepreneurs to start delivering those services privately — that is exactly where a lot of white wealth comes from.
In all, a weird (and regrettably surely not sustainable) sort of win-win situation.