Neo liberals want to leave the nation state ause it doesn't seem like very much. They propose this division between a global order that protects the economy from the interference of nation state governments. And then there the other part of that division is what you describe as culture, which would still be in the purview of the nation state.
Featuring Quinn Slobodian on his book Globalists: The End of Empire and the Birth of Neoliberalism. The story of neoliberalism’s Geneva School—including Ludwig von Mises, Friedrich Hayek, and Wilhelm Röpke—and their vision for a new global order to protect the market from democratic forces in the metropole and across the decolonizing world. An interview from archives first conducted in November 2018.
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Check out these Haymarket titles:
Keywords for Capitalism by John Patrick Leary haymarketbooks.org/books/1886-keywords-for-capitalism
Struggle Makes Us Human by Vijay Prashad haymarketbooks.org/books/1869-struggle-makes-us-human