Traditional Rationality is phrased in terms of social rules, with violations interpretable as cheating—as defections from cooperative norms. If you want me to accept a belief from you, you are obligated to provide me with a certain amount of evidence. If you try to get out of it, we all know you're cheating on your obligation. A theory is obligated to make bold predictions for itself, not just steal predictions that other theories have labored to make. A theory is obligated to expose itself to falsification—if it tries to duck out, that's like trying to duck out of a fearsome initiation ritual; you must pay your dues.
Traditional Rationality is phrased similarly to the customs that govern human societies, which makes it easy to pass on by word of mouth. Humans detect social cheating with much greater reliability than isomorphic violations of abstract logical rules. But viewing rationality as a social obligation gives rise to some strange ideas.
For example, one finds religious people defending their beliefs by saying, "Well, you can't justify your belief in science!" In other words, "How dare you criticize me for having unjustified beliefs, you hypocrite! You're doing it too!"
To Bayesians, the brain is an engine of accuracy: it processes and concentrates entangled evidence into a map that reflects the territory. The principles of rationality are laws in the same sense as the second law of thermodynamics: obtaining a reliable belief requires a calculable amount of entangled evidence, just as reliably cooling the contents of a refrigerator requires a calculable minimum of free energy.
In principle, the laws of physics are time-reversible, so there's an infinitesimally tiny probability—indistinguishable from zero to all but mathematicians—that a refrigerator will spontaneously cool itself down while generating electricity. There's a slightly larger infinitesimal chance that you could accurately draw a detailed street map of New York without ever visiting, sitting in your living room with your blinds closed and no Internet connection. But I wouldn't hold your breath.
Before you try mapping an unseen territory, pour some water into a cup at room temperature and wait until it spontaneously freezes before proceeding. That way you can be sure the general trick—ignoring infinitesimally tiny probabilities of success—is working properly. You might not realize directly that your map is wrong, especially if you never visit New York; but you can see that water doesn't freeze itself.
If the rules of rationality are social customs, then it may seem to excuse behavior X if you point out that others are doing the same thing. It wouldn't be fair to demand evidence from you, if we can't provide it ourselves. We will realize that none of us are better than the rest, and we will relent and mercifully excuse you from your social obligation to provide evidence for your belief. And we'll all live happily ever afterward in liberty, fraternity, and equality.
If the rules of rationality are mathematical laws, then trying to justify evidence-free belief by pointing to someone else doing the same thing, will be around as effective as listing 30 reasons why you shouldn't fall off a cliff. Even if we all vote that it's unfair for your refrigerator to need electricity, it still won't run (with probability 1). Even if we all vote that you shouldn't have to visit New York, the map will still be wrong. Lady Nature is famously indifferent to such pleading, and so is Lady Math.
So—to shift back to the social language of Traditional Rationality—don't think you can get away with claiming that it's okay to have arbitrary beliefs about XYZ, because other people have arbitrary beliefs too. If two parties to a contract both behave equally poorly, a human judge may decide to impose penalties on neither. But if two engineers design their engines equally poorly, neither engine will work. One design error cannot excuse another. Even if I'm doing XYZ wrong, it doesn't help you, or exempt you from the rules; it just means we're both screwed.
As a matter of human law in liberal democracies, everyone is entitled to their own beliefs. As a matter of Nature's law, you are not entitled to accuracy. We don't arrest people for believing weird things, at least not in the wiser countries. But no one can revoke the law that you need evidence to generate accurate beliefs. Not even a vote of the whole human species can obtain mercy in the court of Nature.
Physicists don't decide the laws of physics, they just guess what they are. Rationalists don't decide the laws of rationality, we just guess what they are. You cannot "rationalize" anything that is not rational to begin with. If by dint of extraordinary persuasiveness you convince all the physicists in the world that you are exempt from the law of gravity, and you walk off a cliff, you'll fall. Even saying "We don't decide" is too anthropomorphic. There is no higher authority that could exempt you. There is only cause and effect.
Remember this, when you plead to be excused just this once. We can't excuse you. It isn't up to us.