no one fully knows their own actual biological sex without examining their own chromosomes
That's not true, though, is it.
If you menstruate, you have a uterus, and you are female. If you've been pregnant.
If you have a penis and testicles, you are male. If you've ejaculated.
These are easily observable sex characteristics that don't require a karyotyping test - they're conclusive.
You've not understood what sex IS. It isn't JUST chromosomes. No biologist ever claimed it was.
Most animals have a sex. Plants too.
Male and female isn't just a human condition.
Sex is about how (most) species reproduce. Large gametes, fertilised by small gametes.
We're not a special species in that this happens to us too.
Its never once occurred to me, and I'm sure it hasn't to you, to think "ah, well, now humans have 46 chromosomes. So this person here with 45, or 47 is therefore not quite human. And perhaps they kind of disprove humans exist at all. And perhaps, none of us can ever really be sure we are human. We might be another species. So perhaps we should be much more flexible about considering things like human rights. Perhaps they don't matter, seeing as I'm confused about what a human actually is."
Nope. I know that what is the NORM for human chromosomal makeup, does not exclude the individuals who have exceptional chromosomes. They are still human, because the definition of human doesn't rest entirely upon merely counting chromosomes.
Likewise, the definition of sex does not depend entirely upon chromosomes either.
Sex in humans us determined by whether a person has developed the anatomy to make eggs, or to make sperm. That's basically it. The genetic blueprint of our chromosomes drives this development, yes, but like all instructions, sometimes things don't quite work out.
Whether that anatomical development was halted, or incomplete, or unusual is not of importance in determining sex.
If you have an abnormality of development, you are either female with an abnormality, or male with an abnormality of development.
The existence of people with sex developmental disorders no more challenges the binary existence of sex, than the existence of people with missing or supernumerary chromosome disorders challenges the existence of the human race.