The Equilibrium coalition was a very cynical affair of a number of different groups who didn't trust one another working towards a common goal, which was toppling Doom House. The problem is that NPO was working to establish a postwar hegemony where they would inherit C&G from DoomHouse and turn around and attack their erstwhile allies in the part of the Equilibrium Coalition not controlled by them.
It was for this reason that NPO granted C&G a free hand to counter whoever they wanted without any retaliation. The purpose of this was to enable a dual purpose war, where C&G would be preserved intact, C&G could destroy various elements of XX and SF disliked by NPO, DoomHouse would be degraded (but not badly degraded, there was originally a strict list of who was allowed to attack MK for instance) and the biggest losers of the war would be Polar, XX and SF.
For some reason everyone assumed that the Polar, SF and XX parts would not see through this and let everyone screw us all over. On the day that C&G was countered, NPO actually threatened to switch sides. This is the reason the war ended relatively quickly, as the master plan of Brehon had gone straight to hell. The relatively quick peace was to save C&G, their supposed opponents, from damage.
The cynicism of the war was such that the leaders of Equilibrium were on much better terms with most of their opponents than they were with most of their coalition allies.