About creating your guild : it's very simple.
We return to the situation in the Roman empire, or the middle ages : politicians should no longer listen to scientists at all, so there is nothing to be gained by having scientific analysis turn out one way or the other. Ideally not just politicians, but everybody. Then your club would get back to normal.
The problem is that these scientific analyses carry a lot of weight, and affect monetary outcomes of individuals and organisations by influencing the government.
I would say the big victim of this thinking is not so much the science that goes one way or the other, but rather scientific theories that point out that it's impossible to know certain things. A lot of important sciences exhibit chaotic behavior, like economics, biology, medicine, even climate. This means there are stringent limits to how much we will ever know about them, and that it is perfectly explainable why statistics will (to varying degrees) suddenly fail to work on numbers from those sciences.
But while you can get a lot of money, researchers and positions for investigating why something is true, or why something is false, it's almost impossible to get resources when you claim that humanity as a whole can never make progress on investigating some phenomenon because there's some mathematical rule preventing that. Even in cases where it's effectively an undisputed fact that the central limit theorem doesn't apply, people refuse to accept that things like average do not have a well-defined meaning for things like stock prices, or economic indicators.
This seems to have become a central axiom of modern thinking, that science predicts everything. Even when people know the various basic principles preventing that, like Godel's theorems, or the basic axioms of statistics, they will deny the obvious consequences. Even if we do find the famous theory of everything, we are hardly done. Mathematics leaves a lot of real situations "undecided", and of course reality doesn't leave anything undecided. And even people knowing that you absolutely need the central limit theorem for any statistical rule to apply, refuse to give up their numbers when you demonstrate that it does not apply to their dataset. In most cases, that's easy : you demonstrate that at least one reasonable approximation for their data is a divergent series. At that point you've proven statistics doesn't apply to the dataset. It's easy to do this for lots of data, like stocks (because bad news amplifies, and can kill companies if the amplifier can be > 1, which is easy to find in the dataset), and it's easy to do that once you're outside of a trivially small range, the values of, say, solar irradiance are divergent, which means that whatever the statistical average is up to now, contains exactly zero information. You may as well roll the dice. The confusing thing is that it "generally" works in the short term, which is to say it's a huge effect that has lots of mass and needs time to move around, so it looks like a trend, but it isn't. It's a sudden change taking effect. Like when you have an approaching storm, the variance in any specific location looks like a smooth change, a trend, that lasts days or weeks, but it isn't. It's just the effect of a binary event that is the storm passing through, there is no trend.
We have collectively decided as a species that science answers every question definitively. Even if science itself proves that to be false.