I would think it would be pretty obvious why theism is always the example used. Standard human in-group/out-group dynamics and similar psychological factors. Unlike merely being of a different religion (at least in the US) being an atheist often comes along with (even causally triggers) a certain degree of alienation from many others in society. This alienation drives atheists to strongly signal group membership when around others of their kind and gives them a strong need for reassurance that indeed they are the ones in the right not the majority. Additionally atheism is the sort of topic where people feel the situation is so transparent and clear there ought not to be any question about the conclusion.
As to the Austrian school of economics (or hell the public choice econ class I took in college that had us constructing proofs about which preference axiomitizations are equivalent with and without the axiom of choice) they are right in that pure stipulative mathematical exploration can sometimes be a useful practice even in an empirical science. After all what is statistical thermodynamics than a purely mathematical and stipulative piece of physics.
The issue is that to be useful you also need to have bridge laws (which often go unstated) that govern when it’s reasonable to assume the model assumptions are good idealizations of the real empirical phenomenon.
It seems to me that the basic irrationality implicated here is the assumption that there is such a thing as rationality.
Alright, I just wanted to put that in a clever contenentalist sounding quip but didn’t quite manage. What I mean is this: It (usually) makes sense to talk about beliefs being true or false. We can even talk about tendencies as being more or less inclined to reach true beliefs (given background assumptions about the distributions of such truths). However, implicit in this post and many of the comments that follow is the idea that rationality is some kind of discipline that can be followed and applied.
Or to put the point differently I think many people here are making the implicit assumption that there is some objectively correct way to evaluate evidence (over and above the constraint of simple logical consistency). However, it’s an entirely contingent fact that the sorts of rules we use to predict events in the world around us (scientific induction) actually succeed instead of a world where counter-induction holds (the more times a simple seeming pattern has occurred in the past the less chance it will occur in the future).
Worse, even if you believe that there are some magic objective facts about what the ‘right’ epistemic responses are to evidence at best rationality is a term that can be applied to a particular description, not to a person or a person’s actions. To see why note that I can always describe the same actions by an infinite number of possible rules. For instance suppose my friend asks his computer to spit out a random claim about number theory and decides to put total faith in it’s truth despite a widely accepted supposed proof of the converse. Sounds super irrational but yet the same behavior is also equally well described as saying my friend was following the rule of believing claim X about number theory with probability 1 upon first consideration. Since claim X is in fact a theorem that rule is perfectly rational.