Indeed, it’s completely obvious that absent the Christian faith, there would be no liberalism at all. No ideal of universal human rights without Jesus’ radical upending of social hierarchies (including his death alongside common criminals on the cross). No separation of church and state without the gospels’ “render unto Caesar” and St. Augustine’s two cities. No liberal confidence about the march of historical progress without the Judeo-Christian interpretation of history as an unfolding story rather than an endlessly repeating wheel.
And what’s more, to me, contemporary liberals’ obsession with the supposed backwardness of Christian sexual ethics—an obsession that far outstrips sex’s actual role in the preaching and practice of Christian faith—reflects a subconscious liberal knowledge that Christianity is their theological mother, and they’re its half-rebellious child. You can see in it the child’s characteristic desire to finally overthrow the last bastion of parental authority, joined to a continued desire for the parent’s approval for their choices and beliefs.
It's not completely obvious to me: Douthat wants to reduce the entire history of ethics to Christian ethics, and conservative Catholic ethics, at that. But it seems to me just as easy to get liberalism out of, say, Judaism (see Walzer's Exodus and Revolution as a test case), or, as Peter Euben has argued, out of Greek drama. Not a straight path historically, but not entirely out of the question either. And this is to say nothing of the actual influence of Jewish, Islamic, Greek, and other modes of thought, without which quote-unquote 'Christian' ethics would not have some of their characteristic features (see, e.g., 'virtue ethics'). And, yet further, while some of the founding figures of liberalism were certainly Christians--Locke springs to mind--they were certainly not orthodox Christians, or at least not orthodox in the sense Douthat wants. And let's not even talk about, say, Spinoza. The idea that much of liberalism emerges out of Christianity seems to me to be correct; the claim that this means it is nothing but a weakened form of Christianity seems obviously wrong.
Ross is certainly correct that we owe a debt to thinkers in the Christian tradition—who in turn owe one to pagan thinkers of ancient Greece and Rome—but it’s far less clear that the value of their contributions rests crucially on their theistic metaphysical trappings. Aquinas thought that moral law could be derived by human reason from reflection on natural facts. John Locke may have peppered his political philosophy with a generous dose of theology, but it’s not at all obvious that what was always most interesting and compelling in his arguments requires supernatural support. For that matter, Newton was famously quite devout, and thought the physical laws he described ordained by God. But it turns out that F=MA even after you reject that premise: Physical law (like moral law?) does not require a lawgiver. None of which is to deny there’s plenty of hard problems left for modern moral philosophers to solve, but they’re mostly problems that were obscured rather than seriously addressed by theology.
The Locke sentence seems to me to be an actual, no-fooling case of begging the question: by stipulating that it's only what is "most interesting and compelling in his arguments" that matters, and allowing this to be, one presumes, those matters of greatest intellectual interest to Sanchez, then it's obvious that this will not include any of his theological reflections because they are assumed at the beginning to be additions that obscure, rather than 'seriously address,' moral questions. Walzer, to bring him up again, has a sentence near the beginning of "The Problem of Dirty Hands" in which he says "if popular attitudes are resistant to utilitarianism (and they are), there might be something to learn from that and not simply something to explain about it." It seems to me the same applies here: if the greatest minds in moral philosophy for a thousand years or more think that theological matters have some bearing on moral matters, there may be something to learn from that other than claiming that they obviously have not understood the point of the Euthyphro.