But one of the biggest problems is that people hear things like "eight sexes or one is just as valid as two" as saying that the regularities aren't there. It doesn't necessarily occlude our ability to see the regularities but unless it's very carefully explained--which you did not do--it occludes your ability to express to others that you see that there are regularities.
In a climate where "The libs are insane--they want us to believe there's no such thing as men and women: that men are women and women are men when they say so" is considered a clear and definitive argument against trans identity, failing to declare that the obvious is obvious is an unwise strategy.
I'm not pushing back on the intertwining of sex and gender. Indeed, I'm not sure I even accept that "sex" and "gender" are good category labels because there's so much intertwining both in language and in reality. (Let's cluster that one, hm?) However, I at the very least accept that we can establish a sex-gender axis, and there is a lot of biology we can talk about on one end of that axis that really isn't impinged upon much by culture, and a lot of culture on the other end that isn't impinged upon much by biology except inasmuch as people are the substrates through which culture is expressed.
My point is that if Stock, or anyone else, wants to claim a fundamental dichotomy in the biology, they're correct: it's there. It's not perfectly clean but it's there and it's pretty clean (and Stock seems to admit the lack of perfect clarity). This is something that can be granted with enthusiasm. Making any sort of argument that an actually quite clear division should be obfuscated because the obfuscation achieves some social goal sounds very Orwellian. No--it is very Orwellian.
The place where Stock's argument fails, if it fails, is as you draw back from the "biological sex" pole towards the "cultural expression of gender" pole.
Yes, women tend to be XX, and tend to menstruate, and tend to be less violent (probably biologically as well as culturally--if it turns out not, we can drop this off the list), and tend to be smaller, and tend to have less upper body strength, and tend not to get chest pain with heart attacks, and have a higher risk for breast cancer, and so on and so forth. You can read that off the "sexual dimorphism" part of the biological-sex pole.
But does it, from all that, follow, say, which bathroom a trans woman should use? Does it follow from all that whether or not someone with gender incongruity should get treatment?
The reason why I think this is by far the weakest of your set of articles is that this is the real problem with Stock's position, and you barely touch on it, instead making pretty good points that nonetheless give the impression that you at least wish you could deny an obvious biological fact, in a context where the primary vector of attack is that trans people deny obvious biological facts.
Even if you turn out to be correct, why bother? Why not go for weakest part of the chain of reasoning?
Observing that men and women are different neither tells you what to do in cases where the classification isn't crisp (regardless of whether you deploy additional labels or not), nor does it tell you in most cases what rights someone should have.
For instance, sex-based-rights folks could make case that women deserve certain special rights due to their critical and very difficult role in reproduction. These rights, one might argue, shouldn't apply to trans women who, if they reproduce, get the male easy-mode version. But then what do we do about cis women who cannot or choose not to give birth? Do they also not deserve these rights? And if we extend it to them, why not extend the same rights to trans women as well?
The problem isn't the clustering. Lots of methods with lots of different selections of data will give two main clusters. The cultural examples you gave with supposedly different labels actually drew the main two clusters the same way we do, for instance. Maybe some algorithms with a lot of neurological data as input will cluster trans women as women biologically. Maybe not, and suppose every culture always draws the same boundaries when given a two-alternative forced choice task. Even that doesn't matter! The problem is reasoning from the cluster-label alone to anything else without examining that the reasoning works for all the boundaries (whether sharp or fuzzy).
"I came up with two labels"--great, nice simplification!
"Now I can throw away all other information and never use it again"--wait, what?!