Re: Biological sex — The best description I’ve read of the biological binary drills down to what sex cells a person produces, will produce, could produce, or did produce. And it makes sense because the function of binary sexes is reproduction.
Some do/will/could/did produce sperm. They are male.
Some do/will/could/did produce ova. They are female.
Some do/would/did produce neither. They are classified by their particular genetic variant.
No one produces both.
Re: Gender — Performance of male or female stereotypes.