I thought @amphibious-thing had prepared me for how bad Delaney's chapter on d'Eon would be, but... hoo boy. There is genuinely too much to critique without writing a chapter of my own, so let me first point you to @amphibious-thing's posts about it here and here and here – to sum up her points, Delaney doesn't know shit about the context, nuance or previous research of this topic.
(At one point, he uses a quote from 1716 to make a point about the 1770s. That's like someone using a comment from 1970 to make a point about gender stereotypes today – i.e., disingenuous, inaccurate, and frankly laughable. He also accuses historians of peddling "modern sureties", as though he himself is not a gross perpetrator of presentism when it suits him.)
I know fairly little about d'Eon, but even I can tell Delaney is cherry-picking materials that help make his point – the point being a truly loony theory that d'Eon was basically blackmailed into crossdressing as a woman despite "his" wishes in a grand conspiracy, as a form of psychological torment and retribution in exchange for being allowed to return to France, and just decided to go along with it. Apparently, living under the shadow of scandal and intrigue in England carried a higher cost than surrendering "her very identity" to become a man-in-women's-clothes in France. In all this, we have to put aside the outrageous supposition that Louis' secret agents couldn't come up with a different, more politically relevant and damning accusation to levy against her – surely, if you're trying to discredit someone's character, "uh, actually, he's a woman" is a bizarre place to start.
Unfortunately for Delaney, this theory doesn't make sense even with the evidence he himself provided, viz. that d'Eon continued to voluntarily live as a woman, including referring to herself in the feminine, wearing women's clothes when she returned to England (i.e., was no longer on French territory and didn't have to abide by Louis' rules) and cohabiting with another unmarried woman who was not her relative, something that would have been truly scandalous if anyone thought she was a man.
He tries to eat his cake and have it when sourcing from d'Eon's fictionalised autobiography – the parts that serve his narrative must be based in truth; those that don't are obviously fabrications. He point-blank ignores any instances where d'Eon expresses joy in her female identity.
Delaney claims to have made a grand revelation in finding newspaper extracts that indicate d'Eon did fencing demonstrations in her Captain of Dragoons uniform, trying to sell this as proof that she didn't always wear women's clothes – yet is somehow completely oblivious to the reasoning that d'Eon was a performer with a unique selling point, and that the adverts continued to use female pronouns for her. Delaney says that "This overlooked evidence demonstrates that previous assumptions that d’Éon dressed exclusively as a woman after she returned to England are incorrect" – except this 1) is not overlooked, and 2) is not evidence of what he's claiming. A stage costume (!!) should not be used as proof of someone's inherent gender identity, nor does it negate the choices she made the rest of the time. Delaney claims it would have been "impossible" for d'Eon to continue wearing men's clothing in the early 1770s if she'd been revealed to be a woman; yet here she is, wearing both men's and women's clothing. So, maybe it's not impossible...?
Amazingly, it seems that 18th century people were better able to wrap their heads around a woman contextually wearing men's clothes than Delaney himself.