And anyway, G. E. Moore invented the term “naturalist fallacy” to label philosophers who disagreed with him about morality.

No, he didn’t.

Moore coined the term “naturalistic fallacy” to describe a particular kind of move in ethical argument, which Moore believed to be fallacious. (Specifically, an attempt to establish a substantial ethical conclusion by equivocating between a statement of the form “Everything that is X, Y, and Z is good” and a definition of the form “‘Good’ means being X, Y, and Z.”) His issue with the naturalistic fallacy is meta-ethical, not normative; it’s not that he disapproves of the conclusions drawn from it, but rather that he disagrees with the way they are drawn. (He argues that this kind of maneuver tries to resolve substantive ethical disagreements on the cheap, by changing the subject from ethics to semantics, which fails to offer an ethically serious inquiry, i.e. one which might possibly result in reasons for action.) He did not accuse all philosophers who disagreed with his own ethical views of committing the naturalistic fallacy. In particular, he specifically argues that Henry Sidgwick did not commit the naturalistic fallacy in his ethical arguments, although Moore disagrees with, and spends half a chapter arguing against, Sidgwick’s hedonistic view.

Thus, while I don’t know what Arthur meant (and I see he has replied but I’ll take a gamble and submit this without reading his reply), as I understand him what he writes is not only true but trivially true. If something is natural in the sense of natural law, i.e., if it occurs in the absence of a state, then it is trivially true that in order for it to stop occurring, a state is necessary.

If that’s what Arthur means (I think it’s still not especially clear from his response), then he is either walloping a strawman or asserting a strong claim without evidence. If the argument started out about whether gender roles are or are “socially constructed” or “natural,” then the latter presumably refers to those things which aren’t derived from social construction (which may be a coercive process, a non-coercive process, or an admixture of both), rather than to those things which emerge spontaneously in the absence of coercion. If his claim is the trivial claim you attribute to him (that things that emerge spontaneously in the absence of coercion will emerge spontaneously unless coercion is applied), then he’s not successfully responding to Francois’s expressed concern. If, on the other hand, his claim is the substantive claim that things that aren’t socially constructed cannot be limited or eliminated without the use of coercion, then what he’s saying is responsive, but it’s also not as yet supported by argument. (And in fact is pretty obviously wrong, if it’s intended as a universal claim.)