short answer: the matrix is gender.
but it also represents any social construct pretty generically, and that's why there's so much confusion.
long answer: duck duck go matrix transgender.
also, like, when a creator tells you their work means a thing, just take them at their word. they would know. you can criticize how well or how poorly it conveys the meaning, or explore what subterfuge is concealed within, but questioning explicit intent is a bit silly.
This is reductive.
You advocate a highly intentionalist interpretation of a work - the author says it means this, so that's what it means.
'jevoten and others in this thread advocate a more formalist interpretation - the meaning lies in what is written.
I drew your attention to a more reader-focused perspective - that meaning comes from the reader's experience of the work, not the work or the author.
To say "they would know" is to sidestep this entire discussion and suggest that there's some objectively correct way of interpreting a text and that correct way is intentionalism. This is reductive because it ignores the reality that many people (theorists and non-theorists) don't put a whole lot of stock in authorial intent.
I'm not questioning their intent, I'm questioning whether they successfully expressed that intent in the movie.
Trans people noticed the parallels. I don't think they intended everyone would. They wanted to do more with it too. Switch's Matrix form was supposed to be male.
As Don Quixote once said "El Oh El"