From what I can remember, the simbolism is stronger in the first movie and not so much on the other two. I recall two key things that can simbolize the struggle trans people go through or are references to transgenderism.

• Neo feels that there is something wrong with the world and that he does not belong in it
• The Character Switch was originally supposed to be a man in the real world and a woman when plugged in to the matrix.

I’m sure there’s more but it’s been a while since I came across the analysis.

Worth noting that when I watched the movies I never made an association with transgenderism. I think in great part because I was not even aware of it.