That article fails to explain why White isn't capitalized. It just claims in a very tautological manner that "capitalizing the word in this context risks following the lead of white supremacists."
White people, at least in America, aren't a group with shared culture. The only thing that really unites them is the color of their skin. White people also tend to have an actual ancestral culture they identify with highly-- usually the culture of a European country their predecessors emigrated from. And as far as I know the vast majority of them don't want to identify as 'white', as they value their ancestral culture more.
Whether you agree with that or not is one thing, but I'm not sure why you're ignoring it.