Wanted to come back to this after getting about halfway through the book so far, as well as finishing What Is Politics' series on the book (which, it turns out, only focus on the first 3 chapters). My conclusion is: they're kinda both right.
As someone who has never looked into anthropology, Dawn of Everything showcases some incredibly valuable history that I likely wouldn't have stumbled across by myself. The historic debate with Kandiaronk and his background in particular was exceptionally cool to read about, and the breadth of examples Graeber and Wengrow have to show all in one place is astounding.
What Is Politics' critique, though, does have merit IMO. There are a fair amount of times Dawn of Everything either misquotes, misleads, or withholds relevant context of the hunter gatherer tribes and cultures they reference. As an example, David & Wengrow suggest that cultures which experience only seasonal hierarchy are proof that these ancient cultures experimented with different forms of structuring society, but they left out the parts of the studies they reference to make those claims that show those seasonal hierarchies are absolutely not a conscious choice, but one that is quite clearly something the people being dominated by the hierarchy tolerate only due to environmental circumstance.
As an example, Marcel Mauss's study on the Eskimo: The Inuit experience somewhat egalitarian lives during the winter, and a more strict hierarchy during the summer where things become decidedly patriarchal, as the hunting men have full domination over their families. This is not out of choice by the women, but due to the seasonal change forcing their food supply (which concentrates in the winter) to disperse during the summer, leading individual families to venture out alone to continue to hunt game. This isolates women from their families which would normally act as a power equalizing effect against abusive or dominating husbands. The patriarchal domination does not appear to be a willing choice or experiment in any practical sense.
I also think it's odd that they seem to be suggesting that personal choice is what ultimately caused these egalitarian outcomes, but then also mention materialist reasons for why a culture might've stayed egalitarian, such as their reference to one tribe's use of a constantly shifting fertile river bank for agriculture as not lending itself to laying down territorial claims, which likely aided that culture in not becoming hierarchical.
What is Politics definitely is hyper materialist, but I think he makes a solid case in many of his critiques. His materialism does, however, seem to blind him to the solid argument Dawn of Everything makes that culture and conscious choice does seem capable of playing a large part in shaping society, such as the case of the differences between the Californian and Northwest coast native American tribes.
Without having finished the book, I can't make a final conclusion. But at least from what I've read so far, I'd put forward that environmental conditions do seem to have a not insignificant influence in determining whether an ancient society will lean toward becoming hierarchical or egalitarian, simply due to the conditions being more or less favorable to a group or individual gaining a foothold over others due to resource access. But culture and choice seem capable of playing a large part in that outcome as well.
I think ultimately Dawn of Everything is going to result in more regular folk becoming aware of the facts that our ancestors were fully capable of egalitarian societies and that it was in fact the norm until recent history, which is a terrific boon, and I'll certainly continue to recommend it for that reason alone. Though I think What is Politics' series is also enlightening, and a good companion piece to the book to fill out areas that Graeber & Wengrow likely got a bit wrong just due to the sheer size and complexity of the project.
Interesting, by your guidelines, there's quite some limits on expressing oneself to appease people who can easily avoid and skip over a clearly labeled piece of content.
From my perspective, it's as though someone came into a tavern and, fresh ale in hand, overheard a political discussion happening in a corner booth. Perhaps the subject was particularly distasteful to this theoretical tavern goer, and instead of ignoring it or moving to a seat where they can't hear it, they instead march up to said booth and demand these booth talkers cease their discussion immediately, explaining that they come to the tavern to relax, not have these political ideas pop up everywhere they go.
I suspect the people in the booth would be quite bewildered as to why this theoretical person is going to such trouble to involve themselves in ceasing an activity they could so easily avoid.