Actaea

In any case, I've read about it now. The Security Council passes resolutions, and they are binding.
In the context of our game, joining two Security Councils means you won't be able to fulfill your commitments.

Well, they can't force a war; they force peace. Two resolutions prohibiting aggression or, say, refusing to use chemical weapons cannot contradict each other. That's one thing.
Secondly, the Mushroom People emphasized that the first Security Council didn't exist and still doesn't, because many countries were initially excluded from it. In other words, this means that the first Security Council is essentially powerless. It won't be able to do anything if, for example, the Steelmen start open aggression. It won't be able to negotiate; at best, it will send a contingent there (if the first Security Council even has such authority, which it probably doesn't). In other words, it's essentially useless. As a place where people can discuss and agree on certain treaties, it's fine. But as a governing body that could somehow regulate the military situation, it's not.