In my post about gender identity politics, I explicitly left out any mention of intersex people. This was in part because I didn't want it to become too long and in part because in a way mentioning them is a derailment of the topic, since transgender people are generally not intersex.
But for completeness' sake, here's a summary of how, in my gender abolitionist perspective, intersex people fit into the whole picture, and why their existence is no reason to muddy the definitions of "female" and "male" as designations of biological sex in humans.
In the original post, I asserted that people are split into the exclusive and presumably unambiguous categories female and male, and assigned to a class in the patriarchal gender hierarchy based on this factual birth condition of theirs. This is wrong when it comes to intersex people, since they are not unambiguously male or female like most people are.
I would categorize intersex people into two groups, regarding this topic.
Firstly, there are those who, upon birth, have ambiguous genitalia. The doctors/parents make a conscious decision on which sex they want to assign to the child, and possibly surgically modify the child's genitals to fit to the sex the child is assigned to. In this case, this assignment is what determines whether the child then belongs to the female or male social class.
Secondly, there are those who look unambiguously like one sex, even though they have an intersex condition. For instance, genetically male people with Complete Androgen Insensitivity Syndrome (aka CAIS) are born with a vulva, develop female secondary sex characteristics, and so on; they completely appear female. (Though they have internal testes instead of ova, so they don't menstruate, thus discover themselves to be "infertile" if they remain unaware of their condition until puberty.) In this case, the person is of course assigned to the sex they appear to have; everyone believes them to be genuinely of that sex until maybe it's discovered one day that it's not the case, and even then it's likely that they will continue their life being seen as simply female by society.
Both of these cases involve people who are assigned a place in the patriarchal gender hierarchy not because of the material fact of their sex, but because of a decision made by parents/doctors upon birth of the child, and/or what sex society perceives them to have throughout their life starting from their childhood. This reveals that sex can indeed, in some sense, be viewed as a social construct. Just not in the sense gender identity activists would have it.
And for the largest majority of people --intersex people are at most 1% of the population-- sex continues to be a concrete, unambiguous, material fact of their biology: they either have XY chromosomes, primarily produce testosterone, have male genitalia, produce sperm, etc. all together; or they have XX chromosomes, primarily produce estrogen, have internal and external female genitalia, produce ova, etc. all together. No mixture of traits, no ambiguity. Sorry to disappoint I guess.
(What does differ and mix is things like height, weight, body proportions, amount of body hair, levels of aggression or tons of other personality traits, and so on; these are physical or psychological sex stereotypes rather than concrete facts of sex, and surely we want to grind these stereotypes to the ground, and cut off our collective mental ties between e.g. having testes and being big, burly, and active, or having a vulva and being small, frail, and passive.)
For this reason, intersex people don't pose a reason to redefine "female" and "male". They aren't covered by the dichotomy, but that's because they are truly exceptional people (not a bad thing!), and not because the definitions of female and male are somehow wrong.
Furthermore, transgender people are not intersex. Saying that a transgender man or transgender woman is male or female respectively makes even less sense than to suggest some change to the words based on the existence of intersex people. (A transsexual person may of course have some male/female traits based on physical characteristics they gained through transitioning; that's beside the point.) Gender identity politics would want us to see e.g. a person who has XY chromosomes, primarily producing testosterone, has male genitalia, produces sperm, etc. to be literally female if this person "identifies as a woman". That's a bit of a strange notion, to say the least, and certainly disrespectful to the actual female class of people who are facing oppression based on this birth condition of theirs (and the small minority in whose case it's not a concrete birth condition but was rather assigned to them by society).
Fin.