This is their modus operandi. Deny everything that doesn’t fit their world view or makes them look bad. Not even hard data or science is safe.
I think it's even simpler than that. Deny anything that is a threat to their power/money/hegemony. Their are plenty of people who will do and say anything (even if they don't believe it) for self gain. It's basic short-term vs long-term thinking. They stand to gain much in the short term and lose nothing in the long term because they'll all be dead when it comes time to collect. Combine this with loose ethics/morals…
Truth is a terrible signal, if our group says that Dinosaurs died out 65 mission years ago, and humans rose about 100,000 years ago, anybody can pretend to be a member and agree with us. There is no cost to saying the truth.
And if your group’s beliefs are the same as every other group’s beliefs, there are no “switching costs,” so your members can leave easily. You have a really porous border between your group and the rest of the world.
But if we say that the Earth is about 6,000 years old, and humans rode dinosaurs, and there were unicorns, but they died because they didn’t board the Ark, and so on, well, you sound ridiculous to people outside of the tribe when you say that.
Saying that has a real cost, so saying that proves your loyalty to the group and by virtue of lowering your standing outside the group, drives you to seek your comfort and standing from the group.
I am not putting it rigorously, but it boils down to the fact that humans want to belong to groups, and groups that organize themselves around things that are untrue (or at least rejected by all other groups) generate more loyalty and more of a “we versus them” dynamic than groups that emphasize truth and uncontroversial beliefs.
So it doesn’t even have to be a belief that is self-serving to the group’s leaders (although it doesn’t hurt to have beliefs that the group leader gets all the money and all the young and comely followers as partners).
It’s enough to demand that the group’s members base their loyalty on their faith in beliefs rejected by everyone else.
(None of this disagrees with your point, after all, if a leader bases their power on the size and loyalty of the group, false beliefs are inherently protecting the leader’s power. You don’t need cults to see this. Most companies have a lot of beliefs that every reasoning person can see are false. They know that the diversity initiative is a sham in most companies. They know that “employees are our greatest resource” is said often, but the company behaves like a cobalt mine in the third world, and so on. But loyalty demands that everyone pretend these things are true.)