I think it makes things clearer to compare the arguments of natural law (Straussian Neoconservatism) versus history/tradition (Paleoconservatism) to nature versus nurture, because there is no “versus,” they work together dialectically. You can't leave either history or natural law out of the world view.
But as we endlessly circle the cave of knowledge where the secrets are supposed to lie, Thomas Aquinas reminds us that we can discern only as much as we can discern of universal natural laws using reason or revelation. Natural law now includes the scientific knowledge coming in from sociobiology, in the development of evolutionary knowledge since Darwin. This can be applied to history and natural law.
Survival and reproductive drives adapting to various environments help develop human culture, and in turn the genetic qualities of the people who develop the cultures affect the cultures. Natural laws leading to natural rights need to be in harmony with these natural drives if we are to work in harmony with real human nature and nature.
With universal laws regarding religion I include the intellectual intuition and faith (revelation) in the goal of the evolution of material life to supermaterial Godhood, which can then help ground social philosophy and natural rights. The Inward God is seen as only symbolic of the Outward Godhood reached by material evolution, which gives religion a more natural connection with universal natural laws.
Then there is the further advantage of making reality clearer and more natural with grounding the Platonic/Revealed Religion abstractions of God, Being, or Virtue---which are only definitions---in the real Natural Object of supermaterial Godhood, reached by natural material evolution.
Political philosophy seeks to harmonize with natural human nature in developing Ethnopluralism, which harmonizes best with primary human nature in being essentially kin-centered, local and group-centered. History (Paleoconservatism), and natural law (Straussian Neoconservatism), and natural rights, can come together in this, as nature and nurture do.