As a disclaimer, I don't like the term "white privilege." It's too imprecise and too prone to misunderstanding. I'm also not a fan of the preoccupation with privilege-talk in some left-wing spaces; too often, people focus on the personal—who is privileged and what that means—as opposed to the institutional and the structural. And on the social media Left in particular, privilege-talk has more to do with status and social signaling—I'm more aware of my privilege than you are—than any program for action.
With that said, I don't think we should abandon "white privilege" as a term or an idea. Instead, it's worth trying to make it more precise, so that we know exactly what we mean when we say it. To that end, I think philosopher Charles Mills gives an exemplary definition in his book The Racial Contract. No, he doesn't use the term, but he all but describes it, and provides a large signpost for how we should use the term in our discussions. Here's Mills:
The requirements of “objective” cognition, factual and moral, in a racial polity are in a sense more demanding in that officially sanctioned reality is divergent from actual reality. So here, it could be said, one has an agreement to misinterpret the world. One has to learn to see the world wrongly, but with the assurance that this set of mistaken perceptions will be validated by white epistemic authority, whether religious or secular. Thus in effect, on matters related to race, the Racial Contract prescribes for its signatories an inverted epistemology, an epistemology of ignorance, a particular pattern of localized and global cognitive dysfunctions (which are psychologically and socially functional), producing the ironic outcome that whites will in general be unable to understand the world they themselves have made.
Part of what it means to be constructed as “white” (the metamorphosis of the sociopolitical contract), part of what it requires to achieve Whiteness , successfully to become a white person (one imagines a ceremony with certificates attending the successful rite of passage: “Congratulations, you’re now an official white person !”), is a cognitive model that precludes self-transparency and genuine understanding of social realities. To a significant extent, then, white signatories will live in an invented delusional world, a racial fantasyland, a “consensual hallucination,” to quote William Gibson’s famous characterization of cyberspace, though this particular hallucination is located in real space.
There will be white mythologies, invented Orients, invented Africas, invented Americas, with a correspondingly fabricated population, countries that never were, inhabited by people who never were— Calibans and Tontos, Man Fridays and Sambos— but who attain a virtual reality through their existence in travelers’ tales, folk myth , popular and highbrow fiction, colonial reports, scholarly theory, Hollywood cinema, living in the white imagination and determinedly imposed on their alarmed real-life counterparts.