It said it was a 21 minute read and I beat that substantially, so if I muddle something, I'm sure you'll correct me.
I don't dispute the claims against essentialism, meaning I don't suggest to be a "woman" there is one particular criterion that must exist else you cease being a woman. My position has not been XX is necessary for all womanhood. In particular, I do consider an XY female gender identified person to be a "woman."
As to the family resemblence argument, that is obviously well known and it's not entirely clear to me what that specifically means other than to say that if things look sort of enough alike then they are sufficiently similar for naming purposes. Obviously it is not limited to how things look, but as to all the things about them, including what they do, how they behave and so on.
Nothing I have read in the article has given me pause to think I've violated any of the principles she's identified, and everything I've said can be described in ways that would be consistent with her primer on lingusitic philosophy. That is, we have a good number of folks who identify as "woman" and we have some dispute among those in the language community as to how the term "woman" is to be used. The author asserts this dispute is contrived by those with a political agenda because it should be clear within the whole language community as to what the resemblance of all the folks claiming themselves "women" to be and that the reference to XX and XY are diversions designed to trounce upon the rights of transsexuals.
I don't agree with this, largely because XY chromosomes, as well as the testosterone that comes from it, the musculature that comes from it, and all the primary and sexual characteristics that come from it, result in a being with a certain resemblance that is of critical enough variance that it does not fall within the resemblance of those with XX composition. It is also obvious that the genetic differences lead to different behaviors, both in physical strength and in emotional reaction. We can debate the extent to which societal factors affect the emotional responses of individuals, but we cannot as to the physical strength issues. I do not believe it ought be controversial that men and women respond differently emotionally due to genetic differences as well, but I expect more dispute in this area than with physicality.
When we wish to use the term "woman" we therefore must do so within the context we're in. To the extent there are irrelevant differences in family resemblance, we can disregard them and refer to them all as women. Such is the case if a female gender identifying XY were working at my office. It makes no difference that she might look or act slightly different from a CIS female because the resemblance would be sufficient enough to refer to her as a woman and afford her whatever rights we typically afford a woman in her situation, including how to dress, how to speak, and so on.
On the other hand, if we're having tryouts for the women's soccer league or allowing certain members into bathrooms or locker rooms, the actual physical appearance and functionality of the person is relevant. At that point, the transsexual "woman" and the CIS "woman" no longer share a family resemblance in the manners relevant to this context. If we do choose, however, to call them both women for politically demanded reasons, we may, but we need not then confuse ourselves that the two are the same for the purposes of affording them the same rights of entry into the same previously separated spaces.
If there were a magic pill that a man could take to transform himself into a perfectly appearing woman with all behavorial aspects of a CIS woman yet the XY were maintained, then I would allow that person full access to the CIS women spaces. This extreme hypothetical is offered to acknowledge that it is not the XX/XY designation that is essential for the CIS definition, but it is the manifestation of that genetic composition that we're looking at. I think it's just a scientific fact that genes are determining these things, and so it's easy enough to refer to the genes as a representation of expected behavioral characteristics, and thus how they will look and act (and what they will therefore resemble).
All of this is to say that XX female gender identifying folks are different from XY female gender identifying folks in certain contexts, enough so that offering them differing labels in is order. Calling them both "woman" results in an imprecise language in certain limited but important contexts, resulting in offering them priviledges not properly due them, and then leading me to ask for a more proper A, B, C, D designation system be used when needed.
And I do realize we can eliminate some of these concerns by building more walls in the bathrooms and gym lockers and perhaps doing away with contests of strength and maybe even stigmatizing those men who insist upon only dating CIS women so we can avoid this dispute. I have misgivings about such a solution, which is a different conversation dealing with pragmatics and the how the rights of the entire community ought be respected, not just a particular minority. I leave that as an aside for the moment, though, and focus just upon the language issues you've brought up.