The act of “shutting down a tangent” will be seen as hostile and a grudge is created. Hurt parties will refuse to or be difficult to cooperate with. Your culture can survive only if there’s a shared commitment to it and people feel like they belong.
Perhaps you would want to shut down “politely” and it’s an art to do it without embarrassing the receiving party? But that means that only people with such political skill/power can take that action.