Eventually, I get to a crossroad: either I accept what these people are saying as right (even when it's wrong and would require some absurd actions on my part), or I navigate to exit that situation so I can minimize my future interactions with those people. If neither are possible, it's perhaps time to find new work. Of course, I'd love to get onto the same page as them. But I think we have to acknowledge that sometimes it's not possible. I say this as someone who believes that he has gotten pretty good at this skill after years of experience.
As would probably be expected, these types of people are lifers at organizations where they have used political means to entrench themselves, and would likely not survive on the open market if they ever needed to look for new employment.