In this scenario, it's not beneficial for Blue to choose random.
As an alternative, Blue can choose either a fixed faction or random + color (without changing).
I propose the following:
1. First, Red decides if they want to play random. If so, Blue chooses the template, and the color changes during restarts.
2. If Red doesn't want to play random, Blue decides – now either they choose random (then Red chooses the template), or the standard option with fixed factions and races is played.
Thus, a player who doesn't want to but is forced to play with random factions receives compensation in the form of the right to choose the template.
I also suggest specifying in the rules whether it's possible to choose a bonus when playing random. There's not much difference; I've encountered both options. The specification is simply needed to reduce the amount of negotiation before the game.
P.S. I thought about it a bit :D. It turns out to be almost random by default, meaning fixed factions are only played with the agreement of both players. This isn't very good; perhaps we should think about it some more.
P.P.S. I think I've got it. Just remove the second point; then, if Red doesn't choose random, Blue (based on the rule that players can change conditions by agreement) can offer Red the right to choose the template in exchange for playing random.