You are making the assumption that everyone reading these statements about "White" and "Black" are American.
Even if it is Americans making these statements in an American context, the Internet and the media broadcasts them to the rest of the planet.
You have to think, not just about whether they make sense in an American context, but also whether they make sense in the non-American contexts in which they are being received.
The National Museum of African American History & Culture is an American institution. The tweeter Bryan York lives in Washington DC.
Your other comment about the Australian experience was interesting and it's useful when comparing the US to the rest of the world. However, it feels like you're trying to say I'm off topic because I'm discussing an American document and an American reaction by using American history.
I'm not saying what you are saying is off-topic. I'm just trying to share with you a different perspective.
This American talk about "whiteness" doesn't just get posted in an American museum. It gets posted on Twitter etc and then people on the other side of the planet read it. And the people on the other side of the planet may understand it very differently. But Americans never seem to think about that. (And I'm not saying the concept of "whiteness" might not have some application or usefulness in other countries, including Australia-but it certainly doesn't have an identical application.)
Or, maybe one is a non-US-based employee of a US-based multinational company, and the company leadership starts promoting all this talk to the entire company, without seeming to ever stop to think about how much sense it makes in a non US-context. (But would any non-American employees dare raise the question of how US-centric the biases of its US-based management are?)
Yes, my relatives in China are amused by this. Most people in most places have defined "racism" to mean the judgment that a person is bad in some way merely because of his or her race, regardless of any personal characteristics. But in recent years, Western leftists have edited the definition to make it race-specific, (un)ironically. You can only be guilty of it if you are white. If you aren't white, no matter what you say about or do to another race, it might be bad, but it can't be racist. The justification is that racism is about power, and whites are in charge, so only they can be racist.
So, my relatives want to know, are the baizuo (white leftists) claiming that in China, nothing white people say about or do to Chinese or blacks can be racist? Or are they claiming that they are actually "in charge" of us in China?
Even if it is Americans making these statements in an American context, the Internet and the media broadcasts them to the rest of the planet.
You have to think, not just about whether they make sense in an American context, but also whether they make sense in the non-American contexts in which they are being received.