What does that entail? Here are some relevant passages from the current Catechism of the Catholic Church, promulgated by Pope St. John Paul II (emphasis added):
The duty of offering God genuine worship concerns man both individually and socially. This is “the traditional Catholic teaching on the moral duty of individuals and societies toward the true religion and the one Church of Christ.” By constantly evangelizing men, the Church works toward enabling them “to infuse the Christian spirit into the mentality and mores, laws and structures of the communities in which [they] live.” The social duty of Christians is to respect and awaken in each man the love of the true and the good. It requires them to make known the worship of the one true religion which subsists in the Catholic and apostolic Church. Christians are called to be the light of the world. Thus, the Church shows forth the kingship of Christ over all creation and in particular over human societies. (2105)
And against the idea that it is best for the state instead to be neutral about the Catholic Faith – not hostile to it, but not being influenced by it either – the Catechism says:
Every institution is inspired, at least implicitly, by a vision of man and his destiny, from which it derives the point of reference for its judgment, its hierarchy of values, its line of conduct. Most societies have formed their institutions in the recognition of a certain preeminence of man over things. Only the divinely revealed religion has clearly recognized man's origin and destiny in God, the Creator and Redeemer. The Church invites political authorities to measure their judgments and decisions against this inspired truth about God and man:
Societies not recognizing this vision or rejecting it in the name of their independence from God are brought to seek their criteria and goal in themselves or to borrow them from some ideology. Since they do not admit that one can defend an objective criterion of good and evil, they arrogate to themselves an explicit or implicit totalitarian power over man and his destiny, as history shows. (2244)
It is a part of the Church's mission “to pass moral judgments even in matters related to politics, whenever the fundamental rights of man or the salvation of souls requires it.” (2246)
Every society's judgments and conduct reflect a vision of man and his destiny. Without the light the Gospel sheds on God and man, societies easily become totalitarian. (2257)
There is also the Compendium of the Catechism of the Catholic Church promulgated by Pope Benedict XVI. In response to the question “How should authority be exercised in the various spheres of civil society?” the Compendium answers:
All those who exercise authority should seek the interests of the community before their own interest and allow their decisions to be inspired by the truth about God, about man and about the world. (463)
Then there is the Compendium of the Social Doctrine of the Church, which teaches that “religious freedom is not a moral licence to adhere to error, nor as an implicit right to error” (421); that “because of its historical and cultural ties to a nation, a religious community might be given special recognition on the part of the State” (423); that “the mutual autonomy of the Church and the political community does not entail a separation that excludes cooperation” (425); and that “the Church has the right to the legal recognition of her proper identity” (426).
Of course, all of these documents also teach that non-Catholics no less than Catholics have a right to religious freedom, and none of them calls for what I have elsewhere called “hard integralism.” But they show that the Church clearly teaches that Catholic voters and politicians can and should be guided by “the true religion,” and not merely by some thin common ground between religions, much less by the even thinner common ground between religious believers and secularists.
These are all post-Vatican II sources. But it’s also a good day to re-read Pope Pius XI’s Quas Primas. Viva Cristo Rey!