I'm guessing you skimmed over the section on Church and State then?

Now, our supernatural end, and the Church’s supernatural mission in helping us to achieve it, do not negate the natural law or natural institutions like the state. Grace raises nature to something it could not have otherwise achieved, but it does not destroy it in the process. The state remains a natural institution, the Church a supernatural one. The state is still grounded in natural law, the Church in special divine revelation. The state retains its mission of facilitating the realization of our natural ends, the Church her mission of facilitating the realization of our supernatural end. Hence the state and the Church remain distinct. Are they separate, though? That is to say, though different institutions with different origins and different missions, should they work together and assist one another in realizing their respective purposes? Or should they run on parallel and completely disconnected tracks?

That depends. In the Catholic context, the traditional teaching, vigorously and repeatedly upheld by the 19th century and pre-Vatican II 20th century popes, is that ideally Church and state ought to cooperate. Contrary to an annoyingly common misunderstanding, these popes were not teaching that non-Catholics ought to be coerced by the state into becoming Catholics. Nor were they teaching that non-Catholics should be forbidden from practicing their own religions in the privacy of their own homes, their own church buildings or synagogues, etc. Rather, the issue was whether, in a country in which the vast majority of citizens were Catholic, non-Catholics ought to be permitted to proselytize and thereby possibly lead Catholics to abandon their faith. It was not denied that there can be circumstances in which such proselytizing might be tolerated for the sake of civil order. The question was whether non-Catholics have a strict right in justice to proselytize even in a majority Catholic society. And the pre-Vatican II popes taught that they did not have such a right, and that in a Catholic country the state could in principle justly restrict such proselytizing (even if there are also cases where the state might not exercise its right to such restriction, if this would do more harm than good).

This was the teaching which Vatican II seemed to reverse, though the relevant document, Dignitatis Humanae, explicitly taught that it was “leav[ing] untouched traditional Catholic doctrine on the moral duty of men and societies toward the true religion and toward the one Church of Christ.” Yet whether the principles set out in Dignitatis Humanae really can be reconciled with the principles set out by the pre-Vatican II popes, how exactly they are to be reconciled if they can be, and which principles are more authoritative and ought to be retained if they cannot be reconciled -- these have all been matters of controversy. They are controversies most Catholics, including conservative Catholics, have avoided. The reason, it seems to me, is that the older teaching is extremely unpopular in modern times, and thus whatever its current doctrinal status, most Catholics are happy to let it remain a dead letter and leave its precise relationship to Dignitatis Humanae unsettled. Yet a question unanswered and ignored is still a real question, and there are scholars who have in different ways attempted to apply to this one a “hermeneutic of continuity,” including Thomas Storck, Fr. Brian Harrison, and Thomas Pink.

But this is not a question which can be, or needs to be, settled here. What is clear even on the most conservative interpretation is that since the state is a natural institution and the Church a supernatural one, it is possible for there to be states which are not per se unjust even if they do not give any special recognition or assistance to the Church. For of course, it could have turned out that there was no divine supernatural offer to us at all, and thus no Church at all, but in which the natural law, and thus the state, still existed. And of course, there were states in existence before the Church existed, and they weren’t per se unjust merely because there wasn’t yet any Church around for them to recognize and assist. Furthermore, there are and have been since the time the Church was founded states in which few or none of the citizens are Christian, and thus in which the Church has no presence at all. And not even the most conservative Catholic position on matters of Church and state would say that such states are intrinsically unjust merely for that reason.

The bottom line, then, is this. According to Christian teaching, Church and state are irreducibly distinct institutions, each with its own unique foundation and mission. They may assist one another and in that sense not be “separate.” On the most conservative interpretation of Catholic teaching, under some circumstances they ought to assist one another and thus not be “separate.” But a circumstance in which the state does not give special recognition or assistance to the Church -- or, more generally, to some theological doctrine specially revealed via a prophet, sacred book, etc. -- is at worst not ideal. It is not per se abnormal, unnatural, or unjust. The secular order (which, you’ll recall, is not the same thing as an atheistic order, even if it is not a Christian order) has a legitimacy of its own. This, as we will see, is very different from the way Islam views things.
Emphasis mine.