Ten Conservative Principles are listed by Kirk in his article based on a book he wrote in 1993. Here’s the list but go to the link for the detail.
First, the conservative believes that there exists an enduring moral order. That order is made for man, and man is made for it: human nature is a constant, and moral truths are permanent.
Second, the conservative adheres to custom, convention, and continuity.
Third, conservatives believe in what may be called the principle of prescription.
Fourth, conservatives are guided by their principle of prudence.
Fifth, conservatives pay attention to the principle of variety.
Sixth, conservatives are chastened by their principle of imperfectability.
Seventh, conservatives are persuaded that freedom and property are closely linked.
Eighth, conservatives uphold voluntary community, quite as they oppose involuntary collectivism.
Ninth, the conservative perceives the need for prudent restraints upon power and upon human passions.
Tenth, the thinking conservative understands that permanence and change must be recognized and reconciled in a vigorous society.
His final para remains the issue since the question remains whether conservatism must be aligned with religious beliefs.
The great line of demarcation in modern politics, Eric Voegelin used to point out, is not a division between liberals on one side and totalitarians on the other. No, on one side of that line are all those men and women who fancy that the temporal order is the only order, and that material needs are their only needs, and that they may do as they like with the human patrimony. On the other side of that line are all those people who recognize an enduring moral order in the universe, a constant human nature, and high duties toward the order spiritual and the order temporal.
Perhaps he’s right about the nature of the division, but if he is, then conservatives will continue to be overrun by secular moralities and competing religious views. One might therefore go further and read Voeglin’s own Reflections on Russell Kirk.