Perhaps all of this is quite a bit less true than when Carl Schmitt, in Roman Catholicism and Political Form pgs. 7-8, , first made these observations. (H/T Faith and Theology for saving me the time it would take to type them out.)
The Catholic Church is a complex of opposites, a complexio oppositorum. There appears to be no antithesis it does not embrace. . . . Ultimately, most important is that this limitless ambiguity combines with the most precise dogmatism and a will to decision as it culminates in the doctrine of papal infallibility.
From the standpoint of the political idea of Catholicism, the essence of the Roman-Catholic complexio oppositorum lies in a specific, formal superiority over the matter of human life such as no other imperium has ever known…. This formal character of Roman Catholicism is based on a strict realization of the principle of representation, the particularity of which is most evident in its antithesis to the economic-technical thinking dominant today[.]
The Church requires a political form. Without it there is nothing to correspond to its intrinsically representative conduct. The domination of ‘capital’ behind the scenes [of modern politics] is still no form, though it can undermine an existing political form and make it an empty façade. Should it succeed, it will have ‘depoliticized’ the state completely. Should economic thinking succeed in realizing its utopian goal and in bringing about an absolutely unpolitical condition of human society, the Church would remain the only agency of political thinking and political form. Then the Church would have a stupendous monopoly: its hierarchy would be nearer the political domination of the world than in the Middle Ages.