“A binding moral order grounded by the Natural Law”. Well, that is mighty vague.
If you say freedom above all is not compatible with it, then I would ask for some specifics: what morals, what order, what natural law.
Freedom should be at the crux of it, but then again, you haven’t specified anything.
In a study for the Heritage Foundation, written more than a generation ago, Russell Kirk/The Conservative Mind; defined and articulated 10 Principles of Conservatism, leading with:
“There exists a constant and enduring Moral order (right and wrong) that governs mankind, derived from the Natural Law. Kirk extracted this Principle from Plato. Other original minds include Aristotle, Cicero, the Scholastics, Locke, Hume, Berkeley, Burke and our founders, among them Jefferson, Madison and Randolph.
Conservatism is ageless wisdom while Libertarianism is a very recent faddish nostrum from the French Enlightenment, promoted by the likes of Diderot and Voltaire.
Consider the Ten Commandments as more than the foundation of Judaeo-Christianity. Aren’t they the rules of right and wrong necessary for order in society, to endure and prosper.
For Conservatism, freedom does not trump right and wrong (the Moral Order) while for Libertarianism it does.