Racism is the practice of including race in the construction and maintenance of social hierarchies defined by legally and culturally enforced norms of dominance and submission. In other words, racism isn't simply about race, per se. It's about power, and specifically power with long-standing support in the customs, laws, and economies of the racist society.
Taking steps to reject that power and the systems that maintain it inevitably means treating people of one race in a way that's different from the way they've been treated to date. A policy that says "we're not going to respect your privilege" is obviously not going to treat everybody equally since not everybody had privilege to begin with. However, it does tend towards a point where, in the absence of engrained racial privilege, a more egalitarian society can emerge.
If you're a decent human being who has privilege but doesn't rely on it, that's a positive development. But if you do count on it - or worse, take enjoyment from abusing it - then this shift will not be as welcome.