And then there are things like "intentionally integrate physical movement into math class". What the hell does that mean?
It is exactly what it sounds like: see for instance
this.
Funnily enough, no it hasn't just been pulled out of someone's backside. There's some garbage in this area out there (e.g. some of the claims "Brain Gym" make about neuroscience), but there's proper supporting evidence of its value as well.
Ultimately, caring about a guide like that is a waste of time. There's an offensively circular logic to it, evident in their definition of white supremacy, which includes in it the belief that "ideas of white people are superior to the ideas of people of color". Ideas being a thing without race, anyone can take on any idea. In a majority white society, if every teacher took on all of these suggestions, they would then be the ideas of white people, and indoctrinating non-white children with them would become white supremacy.
That argument is sophistry: clearly ideas come from places; for a majority white society to take and implement ideas and examples from non-white communities does not automatically make those ideas "white". There are forms of cultural relevance: if black people's interest in country and western is much lower than their interest in R&B, if we want to set a problem around a real-life situation (because such context can help provide relevance, and thus learner engagement), R&B may be better choice than country and western for a majority black class. Or even better, find out what interests are of kids in the class (irrespective of race, class, gender, etc.) and use them rather than attempt to predict.
Again, principles of how to do this are embedded in that document and unsurprisingly are defensible according to pedagogic research.
Critical theories have a bad habit (the purpose) of seeing all things as done for the benefit of those in power. In CRT, if a practice hurts black people, it's explicitly to help white people, but also if a practice seeks to help black people, it's also explicitly to help white people. The only way to be anti-racist is to oppose society as a whole, hence an apparently ethnocentric model of mathematics requires teaching how to "challenge the ways that math is used to uphold capitalist views", which you can do by "eliminating references to money" in word problems.
Specious waffle.
I know you never want to be on the side of the craaaazy right-wingers, but "solve racism by not teaching children how to use money in math class" is not a well-established pedagogic concept.
I'm happy to be on the side of crazy right-wingers where they have a good point. Unfortunately, as so often is the case, they are attacking things they do not understand. There is a tendency of conservatives to instinctively think "what worked for me can work for kids today" and view innovation as trendy and superficial mumbo-jumbo: it is after all the basis of conservative ideology and mindset.
I can forgive you and Hawki and millions more not knowing anything about pedagogy, as you are not teachers and were probably educated many years ago under systems and teachers that were plenty of years behind the cutting edge even at the time. McWhorter, however, appears to be in higher education. He reasonably could and should be aware, and instead he's written what seems to me to be a somewhat ignorant or dishonest criticism. But then I guess he doesn't need to try harder. I am not his intended audience, you are.