I confess that when I saw the original Matrix, the whole black/white thing went right past me. I didn't notice anything. HOWEVER ... in Matrix Reloaded, you cannot possibly escape the message that you mention. The last human city (Zion) is about 95% black. Very Black. Funky, sweaty, dreadlocked black. They are the good guys (which is fine, as far as it goes). The bad guys are about 95% white. Very White. Button-down suit, emotionless, robots. The dichotomy is overwelming.
I'll also point out that there are some helpful computer programs in the movie who appear within the Matrix as humans. Let's see, the top three helpful computer programs are:
Key maker -- Asian gentlman.
Oracle -- Black woman.
Oracle's body guard -- Asian gentleman.
You could not POSSIBLY make a movie which so blatantly painted People of Color as an evil scourge and threat to humanity, with White people as the only hope of saving human civilization. NO WAY.
Don't forget to notice who was running the city though .... that's the funny part.