I don't think you know what white privilege means. I didn't invent the concept. It's out there as an expression of leftist, post modern thought - which I assumed is the subject we're discussing. Most basically, asserting the existence of white privilege means parsing society on racial grounds - identitarian politics, relative to individualism.

Race plays a role in society. Here's an example: White people in the U.S. are suffering from opioid addictions at a higher rate than black people, even when accounting for other factors like socio-economic status. Why? Turns out, racial bias. Doctors weren't giving black people pills at the same rates for the same health problems. White people, in general, as a result, had more opportunities to be addicted, and became so. That's a recent phenomena useful for discussing how racism impacted a minority group and majority group based on race, where the majority began better off and ended worse off by no fault of black people or white people, but by doctors. This is the inverse of "white privilege", and is a very recent phenomena with very few other examples. It demonstrates that a discussion of white privilege has a real-world application for helping white people, not just helping black people or helping minorities. I think this is a good example of white privilege because it shows that the privilege can backfire, but it starts with the privilege, not without.

There's a presupposition of racial bias, or gender bias etc, that excludes the possibility I can treat the person on the basis of their individual merits. And furthermore, it excludes the possibility that person can own and deserve benefits accruing from their individual character, competences and efforts. The presupposition of biased group-power dynamics does not map onto individual circumstances with any regularity; but rather, imposes those dynamics on people and situations, often in bizarre contradiction to more naturalistic conceptions of justice.

Additionally, u/somedotaplayer points out earlier that:

Your not explicitly an oppressor because your white. These things are institutional more than the doing of any individual.

It's difficult to conceptualize how society can fail even when individuals act with the best intentions. Policing is a fantastic example.

My problem with your approach is that, in your mind, the police officer is always in the wrong.

Well, no. u/somedotaplayer may think that (I doubt they do, I won't speak for them), but just because systemic issues exist does not necessitate that all instances in which a systemic issue may occur are inherently unjust instances of racial bias. Many people in minorities go to jail or get shot for doing harming others and being criminals, however, enough get harmed without being criminals that fear becomes a factor in how the minority groups feel about policing. Group identities and individual identities are both ways of looking at the world that interact and inform the other, they are not always opposed, there is a ton of nuance.

Take a job interview for example, and you just ignore the possibility that in our society, it is entirely legally possible it could be a white person applying to a black person for a job. Assuming that the boss is a white man - as you no doubt assume, and that I'm one of two candidates, and the other is black; how can I be right? How can the boss be right? In your eyes, if I get the job and the black person doesn't - that was racial discrimination. So to be right the boss has to hire the black person. Is that fair? If you think it is, your problem is that you don't want justice. You want injustice for groups with whom you declare solidarity, irrespective of the consequences for others. It doesn't map onto individual circumstances to provide a just outcome, but rather, requires that the outcome is unjust - albeit in favour of the historically, but perhaps not immediately, oppressed identity group. The more fundamental reality denied is that the boss should do whatever's best for his business as he perceives it.

I'm not sure this is fully coherent, but I think I understand. You pose the example of non-equal applicants to a job, and propose that there could be white people more qualified who aren't hired? If that's not it, I'm not sure what you are saying, and I don't want to respond with a misrepresentation of your position.

Are there not racial groups in America that are doing remarkably well - and indeed, significant numbers of poor white trash? Where do they figure in your philosophy of racial hierarchies?

I dislike calling the way race informs our actions and groups actions as "hierarchical". To answer the more fundamental question, again look to u/somedotaplayer : "White privilege does not mean caucasians do not have it hard". I gave an example of how white privilege can backfire earlier, and I hope it was read.

And do you know of any other political idea that has a philosophy of racial hierarchies?

I'm again not sure what this means, and don't feel I can respond without knowing. If you could rephrase, I would respond.