There is a lot of dubious supposition and extrapolation in that video which is more to entertain than scientifically inform. But if we feel that needs to be handled or weeded out to ensure there is no 'colour bias'?
Just set it so that you always see your team in colour A while the other team is colour B.
Done, mystery solved. You always see your team as Blue and the other team as red, regardless of which team your are on (no 'Blue team' and 'Red team', only 'Allied Team' and 'Enemy Team'). Tada, problem solved.
I'm going to read up on the points and comments he's drawing from in his video. It's interesting enough stuff as food for thought but I don't find it especially compelling without a whole lot of corroboration and it is, fortunately, very easy to marginalize to meaningless in virtual environments.