I don't know if you can draw those exact parallels, and I think it's trivializing the plot a bit to just "ignore all that sci-fi stuff," but it has been confirmed by the Lily that it was at least partially on her mind when writing the Matrix:

She [Lily] added that she didn't know how present her transness was in her mind as they were writing the movie, but that much of the desire for transformation in the films stemmed from her closeted point of view at the time. [1]

There's a lot to unpack in the above comment, and claiming that being CIS removes all the problems of the world is more than mildly naive as well, but there's for sure a lot of lgbtq+ messaging in the Matrix, and it doesn't take a great leap to see it either.

[1] https://www.npr.org/2021/12/22/1066554369/the-matrix-original-trans-fans-resurrections