In this exposition dialogue between Morpheus and Neo, (almost) every person is wearing only two colors. Black and White. No blue, no green, no aquamarine. Even the things they carry are black and white. Handbags, phones, notebooks, and shopping bags are all just black and white.
People in real life wear many colors. Business men wear blue suits and grey suits and brown suits. Police officers wear blue. Handbags and shopping bags have bright colors and big bright logos to advertise the store names.
We all know the Wachowski's chose details as symbols or allusions to other works. They chose the name of the book Neo uses to hide information for a reason, just as they chose the monosyllabic names for agents, and the names of the other characters for a reason.
Why did they make everyone in the training matrix wear only black and white? Was it a mundane reason like making the woman in the red dress so obvious that she would more likely catch Neo's eyes? Or did the Wachowski's have a more symbolic reason? Is it a metaphor for an idea?
I want answers based on interviews or statements by the Wachowski's, or others involved in making the original movie.
Edit to add: I noticed one woman in the background wearing a gray knee-length coat. You can see her at 1:15 in the video snippet.