“One can change gender, although one can’t always get others to go along with it. One cannot change sex, no matter what.”
That is not entirely true, depending on how you try to define the meaning of sex. For example:
Hormonal sex. Yes, natural and artificial changes in the balance of sex hormones changes secondary sex characteristics and hormonal sex.
Chromosomal sex. Yes and no, some natural somatic chromosomes result in changes of morphological sex, mental sex, and various secondary sex characteristics during prenatal and/or post-natal development. Mosaic sex chromosomes produce a person who is both female and male at the cellular level, where some cells carry female sex chromosomes, some cells carry male sex chromosomes, and the morphological sex characteristics may be predominantly female, male, or a blend of female and male. Such mosaic chromosomal sex may not be subject to chromosomal sex change, yet may be subject to hormonal or other types of sex change.
Morphological sex. Yes, natural and artificial processes can change morphological sex, mental sex, and various secondary sex characteristics.
There are additional categories of sex definitions not used in the above examples.
The only sex that really matters is chromosomal sex. Everything else is just appearances.