In Anthem, the color white is equated with equality, cleanliness, and purity, while color is associated with individuality.
Collectivism means that everyone is the same, and there are no individual choices. Therefore, there can be no color. Color is a way of expressing individuality, and you do not need that in a world where no individual is supposed to stand out.
The sleeping halls there were white and clean and bare of all things save one hundred beds. (ch 1)
When seeing color for the first time, it is very strange. Equality 7-2521 and the Golden One find a house that still exists mostly intact from the Unmentionable Times before everything was so tightly controlled.
The sunrays danced upon colors, colors, more colors than we thought possible, we who had seen no houses save the white ones, the brown ones and the grey. (ch 10)
The metaphor is clear. When you take individual choices away from people, you remove the beauty from the world. What makes us special is not just the things we have in common, but the things that make us different.