Noah at Gideon's Blog notices that this is the interesting question arising out of the Linker-Douthat debate at The New Republic.
Since JFK, no one doubts that operationally secular or operationally Protestant Catholics can be good liberal democrats. But what about those who take seriously the magesterium's authority over matters of faith and morals? Did the problem exist? Did Vatican II solve it?
This was a central issue in Canadian history: the dominant view from Durham to Trudeau was "no." Quebec had to drop its traditional Catholicism (as it did in the mid-sixties) to be properly liberal-democratic. What Durham failed to realize was that French Quebec was not going to peacefully give way to the self-evidently superior Anglo-Saxon way of life. What Trudeau failed to realize was that the only possible replacement for the old Catholic Quebec was ethnic nationalism.
One striking fact about traditional Catholic societies (e.g., Quebec, Ireland, Spain) is how sudden the process of liberalization is, and how quickly those societies settle into an indifferentism about the issues of sex and death the Church is clear about. They seem to pretty clearly vindicate Grant's suspicion that only one of the "religion of progress" and traditional religion could inhabit the public sphere. In principle, perhaps liberalism or libertarianism could be neutral between comprehensive conceptions of the good, but it never seems to work out that way in practice, particularly outside the traditionally Protestant world.