This is how I'm understanding it: Rationality is essentially the practice to value truthful speech. But for rationality to last in any culture, you first of all

This is how I'm understanding it: Rationality is essentially the practice to value truthful speech. But for rationality to last in any culture, you first of all require a gut level propensity to trust complete strangers that they are indeed telling truthful things (rather than to only trust the immediate familiar environment). There is some evidence that the Catholic church did indeed bring this about, possibly mostly by banning consanguineous marriage. This way, people were forced to interact with widely different families, to open to them and to establish a culture of showing kinship behavior to people outside of the family clan. World-wide, you find such societal organization almost exclusively in parts which had substantial exposure to the Catholic church. Of course, the Catholic church was in many ways obstructive to rationality, but it did possibly provide the psychological foundation for it.