The colors simply signal the specific type of compatibility modification they have been given. This allows rapid recognition of specific medical requirements or lack there of.
This allows people to know if it is safe to open the door outside and which people need help if the door was suddenly opened. Or if something leaks or cracks. Or which people can eat which food without issues. Or which people require specific supplements or care. Or can handle sunlight without protection. Or which people you can throw a tool at local gravity without becoming a murderer.
It may also denote legal status. These people were modified to match specific environment before birth. This implies people doing the modification were not concerned about the person wanting to live somewhere else. Sometimes this is because the modification was cheap and safe. Sometimes it is because interstellar travel is expensive. Sometimes it is because the company or the government decided where the person will live before they are born.
The modified colonists would essentially be serfs, living and working where they are ordered to. It would be convenient, and probably legally required, to have easy visual differentiation between people of different legal rights.
Extensive genetic engineering might simply be controversial enough that law requires it to be visually recognizable.
Note that even if such legal requirements no longer exist, people might choose not to edit out or hide their heritage. Seeing who can safely eat food with high heavy metal content or breathe air with chlorine in it is still convenient so why bother. Besides it would dishonor your ancestors.