I was hoping for a concrete example but taken the assertion as true my speculation would be that there probably wasn’t the same civil righs movement historically which were inspired by liberation movements of the times to have objectified themselves partially in such a society as the soviet union.
Added also that liberalisation of Russia seems to have been a delayed process rather than something based in its foundations like with the US.
But im not sure modern marxist reify whiteness too much except to the extent that racial and gendered relations are subsumed in class relations in their own way but that dont take precedence, only help to make clearer the picture of the state of things.
It was my inpression though in not putting class on an equal level as simply a matter of identification on par with racial and gender segregation making their categories significant, marcist types often accused of class reductionism which some likely are, but aren’t necessarily always.
So they might talk of whites having higher status based in the economic stratification along racial or gendered lines. But I dont think white privilege is too strong a concept relative to it being but a part of a broader conceptual scope.