First, the conservative believes that there exists an enduring moral order.
This is the foundational principle of conservatism; as a Christian conservative, I would modify it thus: there is a created, enduring moral order.
The point here is that the conservative is convinced that at least some things in this changeable world are unchanging, and that these unchanging truths are of first importance. Kirk mentions two particular examples: “human nature is a constant, and moral truths are permanent.” Both of these commitments, I believe, are thoroughly biblical.
By way of contrast, the modernist (typically) is committed to some form of empiricism, a trust that truths must be verifiable by testing and sense experience. The problem is that empirical evidence never underwrites a universal conviction; there is always the potential that, after a thousand white birds, the next might be black.
Christians, in particular, are freed from the tyranny of the empirical: where God has spoken, we know, even if we have no independent verification.