Conservatives struggle to accept the objective moral truth of anarchism (and libertarianism, in matters of law) once they see it (and no one can really unsee it), and they continue to cling on to illogical and immoral and ultimately self-destructive and culture-destroying notions such as the Constitution or the idea of a homogenous, even "Christian", culture or nation that can be defined based on geography or national origin or political control.
Speaking from personal experience, I believe there could be several reasons for this immoral behavior (frankly, unrepentant and disobedient, if said conservative also claims to be a Christian). One is the desire to have comforting myths and narratives surround us, that speak to us of a mythical good past. As human beings, this sort of story-telling and campfire mythologizing, even if ultimately untrue and based on false nostalgia, have always helped us cope with the reality of violence and war around us, even when such violence and war is endorsed by our own beliefs and (in)actions.
Related to this false memory of a mythic past, we can also see the resistance to Natural Law arising from the fear of the unknown future. Conservatives, like all people, have been deeply indoctrinated by the State to give up personal responsibility and outsource the important matters of civic life -- justice and mercy -- to powerful people who claim that it is their right and theirs alone to exercise power, pretend to be able to divine the future (even if logic and history contradict this) and practice the important aspects of civic life.
We observe that Natural Law, when disregarded, does not stop being true -- we just experience the deleterious effects of ignoring it, like all other laws. Try walking off a tall building and saying "I refuse to believe in gravity -- Brandon says its quite patriarchal and supremacist to believe in it. I take the more diverse, equitable and inclusive posture of ignoring it and chasing after my dreams". The same principle is seen in the Bible : we ignore God's revelation of His moral law, to our peril. When we desire governments, in opposition to His will, He lets us have that evil desire in full measure, and lets us enjoy the full measure of tyranny, slavery and oppression.
Again, speaking from personal experience, the escape from this mental prison can come when one realizes the truth that no human being (regardless of what they claim and regardless of their power and weaponry) can divine the future and plan society, and therefore no one has the moral right to do so. The only moral responsibility that all people have is to assume personal moral responsibility for one's own life, for one's loved ones, neighbors and community, and to stop outsourcing away the moral duty to practice justice and mercy in one's own rightful domain.