Also, this criticism only really addresses the first, taxonomic part of the book, which was by far the least interesting.
David Graeber is, as far as I can tell, a professor of anthropology. Which means he doesn't have domain expertise in any of the areas he's criticizing. Indeed, I could (flippantly, but honestly) say that I think "professor of anthropology" is a bullshit job, but then again I'm a severely left-brain guy and I'm going to assume there is a social value there that's just going over my head.
To put things another way: my wife once asked me what my interest was programming-wise. I told her it was compilers and programming languages. And she asked: well, don't they have those already? I strongly suspect if people get a 3% exposure to programming (e.g. writing yet another JS framework), like Graeber is doing with the various jobs he talks about, they'd think that programming is also full of "bullshit jobs." But that would be a conclusion arising out of ignorance.
To illustrate with a drastic example: Suppose you have two workers, one who digs holes and one who shovels the same dirt back into the hole to close it. Outside the system, it's obvious that they're not doing any meaningful work. Inside the system, there's probably some argument why these jobs are useful. (Maybe government regulations require that their company dig at least X holes per month. Or you could argue that it's good because it increases GDP or reduces unemployment.)
I'm not going to defend every single professor of anthropology, but "studying human societies and cultures and their development" sounds like a useful thing in general and is exactly what this work is.
He mischaracterized the worth of compliance personnel, corporate lawyers, and PR team members.