That's a good question. I think BG's way of thinking about gender categories is potentially useful for racial/ethnic categories as well, particularly the bit about category membership as a conferred status. I think they'd probably agree with this. They don't really argue that we ought to have gender self ID; they explicitly assume this to be the case, and are more trying to show that it's coherent. I suspect if you asked them they would probably say that we ought not to have racial self ID, or that it ought to be much more limited than in the case of gender (here are some candidate reasons why one might think this https://www.bostonreview.net/articles/robin-dembroff-dee-payton-breaking-analogy-between-race-and-gender/), but they'd probably grant that it is at least also coherent.
Sure, one can always embed a game inside another one and so alter the overall expectation values how one likes. That said, we still only want to play the meta-game if it had positive expectation value, no?
The conclusion seems rather to be "human metabolism is less efficient than solar panels," which, while perhaps true, has limited bearing on the question of whether or not the brain is thermodynamically efficient as a computer when compared to current or future AI. The latter is the question that recent discussion has been focused on, and to which the "No - " in the title makes it seem like you're responding.
Moreover, while a quick Google search turns up 100W as the average resting power output of a person, another search suggests the brain is only responsible for about 20% of energy consumption per time. Adding this to your analysis gives .13% "efficiency" in the sense that you're using it, so the brain still outperforms AI even on this admittedly rather odd sunlight-to-capability metric.
What does quantum entanglement mean for causality? Due to entanglement, there can be spacelike separated measurements such that there exists a reference frame > where it looks like measurement A precedes and has a causal influence on the outcomes of measurement B, and > also a reference frame where it looks like measurement B precedes and has a causal influence on the outcomes of measurement A.
"Causality" is already a somewhat fraught notion in fundamental physics irrespective of quantum mechanics; it's not clear that one needs to have some sort of notion of causality in order to do physics, nor that the universe necessarily obeys some underlying causal law. To the extent that quantum mechanics breaks our common-sense notions of causality, it's only in this very particular sense (where it seems like Alice measuring first "causes" Bob's measurement to take a certain value, or vice versa), and since neither party can use a measurement scheme like this to send information, the breakage doesn't invite paradoxes or any sort of other weirdness.
Outside of philosophical musings about causality (which, to be clear, I think are perfectly valid and interesting) it suffices to say that entangled systems exhibit correlations without a common cause, and leave it at that.
If you're interested in a recent technical discussion of some of these ideas, I recommend the following paper: https://arxiv.org/pdf/2208.02721.pdf
Just to (hopefully) make the distinction a bit more clear:
A true copying operation would take |psi1>|0> to |psi1>|psi1>; that's to say, it would take as input one qubit in an arbitrary quantum state and a second qubit in |0>, and output two qubits in the same arbitrary quantum state that the first qubit was in. For our example, we'll take |psi1> to be an equal superposition of 0 and 1: |psi1> = |0> + |1> (ignoring normalization).
If CNOT is a copying operation, it should take (|0> + |1>)|0> to (|0> + |1>)(|0> + |1>) = |00> + |01> + |10> + |11>. But as you noticed, what it actually does is create an entangled state (in this case, a Bell state) that looks like |00> + |11>.
So in some sense yes, the forbidden thing is to have a state copied and not entangled, but more importantly in this case CNOT just doesn't copy the state, so there's no tension with the no-cloning theorem.
I see the two main arguments of the book as 1) we should understand "gender identity" as a bunch of subjective feelings about various traits, which may or may not cohere into an introspectively accessible "identity"; 2) we can understand gender categories as a particular kind of irreducible category (namely historical lineages) to which membership is granted by community consensus, the categories being "irreducible" in that they are not defined by additional facts about their members. These stand or fall independently of whether we accept gender self-id, although self-id is compatible with BG's understanding of categories in a way that it is not necessarily with clusters.
See the last section of the review for reasons why we might sometimes prefer BG's analysis of categories on the outside view; I think it's potentially more useful for thinking about the role of categories in society and in people's lives. I agree this is not a knockdown case, but I certainly think it's a better framework than e.g. "men are those with the essential spirit of man-ness inside them," which is also coherent but not very interesting.