So it might be the case that bayesian updating has some quirky memetic mutation that could lead it to destroy itself if it stopped working. Maybe so-called 'rationalism' is especially bad at absorbing internal contradictions. But this would be a feature of they belief itself-- not a feature of it being a belief about procedure. Many beliefs about procedure are exactly the opposite-- take believing that truth can be taken from the Bible. That procedure is self-justifying and there is no way to dispute it from within the assumptions of the procedure.
Mostly, I just don't think the distinction you are trying to make between "procedural" and "substantive" beliefs holds water. Beliefs about political theory and economics, for example, are almost all procedural beliefs (i.e. the right procedure for making a law or stimulating the economy). What about them would make them immune to labeling problems?
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The race is not always to the swift, nor the battle to the strong, but that's the way to bet.
-Damon Runyon
Damon Runyon clearly has not considered point spreads.