"I believe the essential difference between the right hemisphere and the left hemisphere is that the right hemisphere pays attention to the Other, whatever it is that exists apart from ourselves, with which it sees itself in profound relation. It is deeply attracted to, and given life by, the relationship, the betweenness, that exists with this Other. By contrast, the left hemisphere pays attention to the virtual world that it has created, which is self-consistent, but self-contained, ultimately disconnected from the Other, making it powerful, but ultimately only able to operate on, and to know, itself." (The Master and His Emissary, Iain McGilchrist, 2009; page 93).
As the frontal lobes operate to oppose, inhibit and modulate the more instinctive impulses of each of the hemispheres so the culture and the social institutional milieu in which human society plays itself out operates to elaborate and extend the experiences of each of the hemispheres.
As media are extensions of the senses so religions are extensions of the Otherness, and so states are extensions of the virtualness. The political/ideological left mistakenly believes the institutions of the state can and should be harnessed to the needs and impulses of recognizing the Other while the political/ideological right mistakenly believes the institutions of the church can and should be harnessed to the needs and impulses of collective glory. Both these political/ideological orientations are simplistic and primitive.
The Bible offers a more evolved, more advanced, more nuanced and more subtle version of how it is the collective, social, institutional, cultural milieu ought to interact with the various experiential modes of each side of the human brain.