I can't speak for white people obviously, but I also believe that we shouldn't judge people by the colour of their skin and I'm not using that as code for "don't talk about skin colour".
We've spent decades talking about colour and people still try to deflect attention from important issues which affect black people. I don't think the issue is whether we talk about it so much as whether people are interested in righting wrongs. Some are just concerned with keeping what they have and getting more. They don't care who loses out in the process. Ask 50 Cent why he voted for Trump for example.
My point here is that everybody is capable of this selfishness. Skin colour is still sadly relevant, because many systems disproportionately target one skin colour. But the skin colour of the people who oppose that injustice doesn't matter at all.