That's basically the same idea as what navies do on aircraft carrier decks: each role wears a different colour basically head-to-toe.

In this case, I think the colours should be more reserved for operational duties - command red, bridge orange, medic green, engineering purple, combat/security black, etc. and anyone else not in an operations role would wear a navy blue and their specific role could use insignia like atomicbocks commented in a sibling to this comment