The concept of transparency, opacity, and mutual (un)intelligibility have already come up a few times. These all get to the core of what a belief system is. While our understanding of belief systems was here constructed out of vectors of participants' opinions, what makes it a system is how aligned and unaligned beliefs allow the participants to interact with each other as a system.
Transparency in the system means that meaning is transmitted with high fidelity between participants. This transmission is typically facilitated by having beliefs in common; shared beliefs form assumptions that participants can take, information that doesn't need to be transmitted in order for the meaning to pass between them undistorted. Note that transmission doesn't always depend on identical beliefs; complementary beliefs are another form that can be transparent. Consider information passing from general to soldier; if the general knows their job is to give orders, and the soldier to take them, then these complementary beliefs enable orders to be passed down. If the soldier, say, were to think that their job is to also give orders, then the orders they receive may be ignored, and the fitness of the army as a whole suffers because of this opacity.
Opacity is the opposite of transparency, a case where mis-matched beliefs cause meaning to be distorted in transmission.
Mutual Unintelligibility is the extreme version of opacity; where beliefs are so out-of-alignment with each other that the result isn't mistaken transmission, but no transmission at all. Though it might seem like a contradictory result, mutual unintelligibility is typically rather harmless; participants that do not understand each other rarely find themselves in situations where they need to understand each other. Consider, if you will, the many ways you don't suffer for not understanding Swahili (even if you do, you still understand the point that I'm making).