Also the thing is just steeped in trans metaphor. Consider the agents deadnaming Neo throughout as "Mister Anderson" Ander being intended as the same word part as Androgens, Androgyny or Misandry... Mister Ander Son. The system keeps reinforcing his identity as Man man man.
Go listen back through Morpheus's speech just before he offers a red and blue pill (back in the 90's horomone treatments for trans women came in the form of little red pills)... It's a sci-fi parable for gender roles and dysphoria. Of being forced into a system where oppression isn't seen or heard or touched because almost nobody recognizes it. Only some nebulous but insistant feeling causes you to want to break free, to explore yourself.
And once you break free you no longer have the protection from the system. The system sees you as a threat. You must accept less resources and support outside of whatever small found family and resistance you gather.
Like all scifi parables some of it's metaphor plays second fiddle to making the technical premise work from a narrative perspective...but whenever they start talking about the Matrix consider they are actually saying "The Bioessentialist construct of gender" and you can see a lot of the different facets behind deliberate creative choices.