OH. Hah, I always thought this was one detail they got wrong for some reason, considering estradiol is bluegreen. Should have considered the context back then.
Smith doesn't represent the system, but the co-opted power structures of the system by a dictatorial force. If you remember, the system wanted Smith dead just as much as it wanted Neo gone.
Taking the red pill (estrogen at the time was a red pill) enables you to see that a lot of society is a facade and there are depths beyond it. In the real world that could be things like learning that there are people and lives that society refused to acknowledge like trans people
Thanks for choosing the right wording! It's certainly one of the ways to read it. And it's also a good idea to sometimes search for a new matrix theory and then doing a re-watch. It is mindblowing how many different, sometimes completely crazy yet beautiful narratives the original trilogy can fit to, all while also being enjoyable as is without any.