Promoting diversity in hiring is like the "women and children first" rule for lifeboats. The existence of the rule does not prove that women and children are tough enough to get their own seats now, it is in recognition that they would get no seats if the men used strength as the sole arbiter of seat selection. Similarly, those questions are an attempt to overcome the unconscious bias of the employer towards hiring able-bodied white people. It is a sign of the weakness of those targeted groups, not their strength.
And "privilege" does not mean that every white person lives a life of luxury; it means only that there is strong statistical proof that on average, a typical white person is more likely to be hired than an equally qualified black person. There are some hard-up whites and some rich blacks, neither of which disproves the stats.