It is not needingly the same. You may prefer a given economical system because you think it better for some reason. Yet with the demonstration an other system would satisfy you better, you could change your mind. That would “just” require a strong rational demonstration.

Religious faith is not rational. It is not based on proof, but purely on feelings… And greatly on the fact all the efforts made for the faith would have beel made for nothing if the faith is admitted false, and therefore the cost seems too high for the believer. So the fact nothing may prove the object of faith becomes a test of faith that justify it.

Yet you also have some rational believes. Even on simple things such as the best way to wash your hands. Should someone demonstrate a better way to do it, we would doubt at first, but if the explaination is clear and proven, we would adopt this new way. And we would not feel a pain at changing. I think this absence of pain is a mark of rational belief.