Even on its own terms, the "white privilege" theory is deficient. In terms of structural aspects of society that perpetuate race-based disadvantages, the main difference isn't between white people and everyone else, it's between Black and Native American people and everyone else:
https://academic.oup.com/qje/article/135/2/711/5687353> White and Hispanic children have fairly similar rates of intergenerational mobility.... Because of these modest intergenerational gaps, the income gap between Hispanic and white Americans is shrinking across generations.... Asians appear likely to converge to income levels comparable to white Americans in the long run.
> In contrast to Hispanics and Asians, there are large intergenerational gaps between black and American Indian children relative to white children.... If mobility rates do not change, our estimates imply a steady-state gap in family income ranks between whites and American Indians of 18 percentiles, and a white-black gap of 19 percentiles. These values are very similar to the empirically observed gaps for children in our sample, suggesting that blacks and American Indians are currently close to the steady-state income distributions that would prevail if differences in mobility rates remained constant across generations.
In terms of rhetoric, moreover, it's deliberately inflammatory. Critical theorist academics appropriated existing terms with weight connotations, like "racist" and "white supremacy," to mean more abstract, systemic things that don't necessarily imply prejudicial intent.
People should be wary of adopting this rhetoric even if well-intentioned. Just because some academics thought this rhetoric was clever doesn't mean that people of color generally want race-relations to be defined by such inflammatory rhetoric. As a purely practical matter, there is a ceiling on the fraction of white people who will actually respond in a productive way to being called a "racist" and a "white supremacist" (even if you explain to them the academic twist on the words). There is a reason we do things the way we do them. There is a reason civil rights movements have been built on appeals to universal values and the goal of color-blind equality as the ultimate ideal.