White privilege exists in majority white cultures (go figure huh?) But travel to Africa and tell me black privilege doesn't exist, or Japan and their toe curling attitude to Japanese superiority, or Arab states etc etc.
If you live in a culture where a particular race is prevalent then you will see it be in primacy, this is irrefutable around the world. Whether it is right or wrong is a different discussion but it does exist.
In the "west" and to be honest it isn't the west really, it is the UK/US and to lesser extents Canada and Australia (though strangely not really all that present in NZ for some reason) we feel we have to fix this without reciprocal efforts elsewhere to address the issue. Go to other western countries such as Germany, France, Switzerland, Scandics and they don't have the extreme self hatred but that is another whole discussion as to why.
Bias is wrong but it exists, sometimes overt and thus challengeable, mostly it is unconscious and nigh on impossible to challenge. Why impossible? Because the agenda from those seeking equality of treatment has shifted from seeking equality of treatment to imposing a disadvantage of those from the primary culture. At this point and it is extremely noticeable and traceable in just the press never mind doing any form of real research, what you get is a backlash and a form of protectionism. The primary culture does not need to "fightback" as actually it's primacy still exists but they feel challenged and as such they fight. The upshot of this is that basic equality and basic rights are being challenged (whereas ten years ago were almost universally accepted) by the majority of a defence mechanism to an over reaching attack from those facing them.
I'm all for all forms of equality of opportunity, equality in itself does not exist (biologically, mentally, physically, emotionally, morally etc) but that does not matter. The world benefits from different cultures, different viewpoints, it adds vibrancy and a unique viewpoint can break an impasse in a problem a particular society cannot in itself solve. We should still allow equality of opportunity but you cannot, and should not, try to enforce equality of outcome. As soon as you attempt to enforce equality of outcome, and the only way to do this is to deconstruct the primacy, you get fools like Stephen Yaxley Lennon and his ilk gaining support and backing by otherwise decent people who are terrified they will lose their opportunities through nothing other than their birth. The far reaches of the liberal agenda are trying to tackle inequality brought about by race, by attempting to artificially disadvantage those of a particular race that they choose not to like. You couldn't make it up.
TLDR, extreme liberals are fools and are creating their own opposition by being too aggressive. Consenus and compromise would be better approaches.