To address the idea of white privilege directly:
- It's increasing racial awareness and conflict.
- It's a blunt instrument that doesn't take into account the myriad of circumstances each individual faces (such as financial wealth, mental health and physical height).
To provide a counter example to parent's, I'd rather be a rich ethnic minority unfairly stopped by a cop, than an ethnic majority person living in a trailer park and addicted to meth. The ethnic bigotry in this example isn't excused, but it's not the main concern.
Perhaps, all else being equal, one could argue that 'white privilege' matters.
But all else will never be equal. And the one place where equality really matters, it already exists - the law.
Notions of privilege could at least attempt a full accounting at the individual level, rather than dictating in broad strokes.
There is no realistic scenario where one civilization does not dominate others.
Macro-history is fundamentally about the rise and fall of civilizations - the undesirable elements of this are consistent, but Western tradition and enlightenment has also given us democracy and science, and put us in a collective position where we are so relatively prosperous that we can look at the past with an inflated sense of shame.