I think the most important part of 5e wizardly schools are the granted powers for the wizard's specialization.
Oh, there's a few oddball references to school in the rules, like the restricted spell lists for the arcane trickster and eldritch knight, but the rest of the references to schools live in the wizard subclasses.
So write some more subclasses.
I don't remember enough about the wizards to recall the associations of the colors beyond Good/Neutral/Evil, unfortunately.
I'd be lazy and partition the school/specialties; Divination is purely White, Illusion Red, Necromancy Black, with the remainders available to all. So an evoker could wear any robes.
You could also look to the paladin (yes!) and extract their oaths into school abilities, since they have a few semi-moral mechanics.
You might be able to get a bit of purchase by using warlocks for all wizards (ignoring what I said above); great old one is White (mind reading and radiant powers); fey is Red (charming/fearing, druidic nature connection); fiend is Black (fire, undeath, destruction).