As a data point, Spike Lee's School Daze had a number of different real NPHC GLOs represented including Alpha Phi Alpha and Alpha Kappa Alpha and I don't believe that an effort was made to have members of the respective real GLOs wear those colors. (See the end of the Alpha Phi Alpha step show at
https://youtu.be/WfPc8Ia7E20?t=84 for characters in Alpha Kappa Alpha wear.