There is nothing in human history tosupport the assertion that the absence of religion equates to something more rational in culture. Period.
This statement is at best true only in the most meaningless sense that it is also true that "nothing in human history to support the assertion that the absence of
frontal lobes equates to something
less rational in culture."
Both this and your statement are only true in the sense that there is no evidence because there have been no cultures with an absence of religion or frontal lobes.
Even cultures ruled by the authoritarian States you list, were filled with people who had religion.
But beyond that, your statement is false because their is plenty of evidence that cultures with less religion are more rational. The progress of the West hinges in large part on rationality which coheres strongly with a corresponding reduction in religious thinking both by the citizens of these societies and by their leaders.
Western governments were designed by people keen on not using religious thinking in the formation of the governments and on keeping the impact of religious assumptions to a minimum. While far from perfect, these systems allow for greater influence of rational thought on the political process than most societies in history. In addition, clear signs of irrational culture among these western nations (such as rejection of basic scientific facts like evolution, human influenced climate change, biological basis of homosexuality, the causes of criminality, etc. ) are strongly predicted by cultural differences in religiosity.
In my view religion is one manifestation of a basic human nature.
This is true, but religion is more than a mere byproduct of a human tendency toward unreason and authoritarianism. Being a cultural system that actively and as its central mission seeks to influence culture and human action and thought, religion is clearly more than an outcome variable. IT is also a causal factor that enables and exacerbates the very irrational thinking that gives rise to it.
Religions of today that dominate do so because they so efficient and effective at having this kind of impact and helping to foster the very irrationality and authoritarianism upon which they depend.
Oh, and as Underseer pointed out, your comments about governments and rationality aren't even relevant to the thread topic which is about religious beliefs held by people and various social ills, many of which may not be due to irrationality so much as the destructive morals and values that most religions promote.