I don't think the OP was agreeing with this stance, only describing it. It seems they probably disagree with it as this is clearly sarcasm given what was just described: "anyone arguing for an identity based on something so superficial as skin colour is probably a segregationist"

Thanks for writing this; this was my take as well (op was full on -mocking- the take being described) and I was surprised to see people think it was arguing for a very clear double standard.

My take: I think that whiteness is not a lack of culture. It is the dominant culture, which makes it feel like an absence of culture to most within it. Like a massive white (pun intended) wall, which makes other cultures clearly visible in front of it.

I would also guess that most people saying that are centrists/moderates cosplaying a different political ideology, making it even harder to see any distinct features or a sense of community and belonging.

I think this is on the right track. There isn't a "white" American English variant -- it's just American English. But AAVE is a thing.