Papal teaching on the fundaments of the Catholic State and opposed to the essentially a-confessional and egalitarian Modern State are summarized in passages from the Encyclical Immortale Dei.
Leo XIII taught that by the fact that authority proceeds from the very nature of society and man, it has God as author. After demonstrating this, he continued: "Hence it follows that all public power must proceed from God. For God alone is the true and supreme Lord of the world. Everything, without exception, must be subject to Him and must serve Him. Therefore, whosoever holds the right to govern holds it from the one single source, namely, God, the Sovereign Ruler of all. 'There is no power but from God' (Rom 13:1)" (n. 5).
The Sovereign Pontiff was rigorous against religious indifferentism: "It is a public crime for societies to act as though God absolutely did not exist. So also is it a sin for the State not to have care for religion, regarding it as something beyond its scope or of no practical benefit, or to adopt from the many forms of religion the one that fits its fancy. For we are all bound absolutely to worship God in that way which He has shown He desires to be honored" (n. 11).
He also addressed the heads of States: "All who rule, therefore, should hold in honor the holy name of God, and one of their chief duties must be to favor Religion, to protect it, and to shield it under the credit and sanction of the laws, and neither to decree or sanction any measure that may compromise its integrity" (n. 12).
Leo XIII's argument on the supremacy of the Catholic Church was irrefutable: "And just as the end at which the Church aims is by far the most noble of ends, so also is her authority the most exalted of all authority, and can in no way be looked upon as inferior to the civil power or in any way subject to it" (n. 16).
He also dealt with the question of the Church having the right to intervene in the State ratione peccati, that is, in those questions that imply sin. He stated: "Whatever, therefore, in things human is of a sacred character, whatever belongs either to the salvation of souls or to the worship of God - either by its own nature or by reason of its end - all this is subject to the authority of the Church. As for other things that fall under the civil and political order, they are rightly subject to the civil authority, since Jesus Christ commanded to render to Caesar what is Caesar's, and to God what belongs to God" (n. 20).
Leo XIII also refuted the fundaments of the Modern State:
The sovereignty of the people: "Now, simple natural reason demonstrates that this way of understanding civil government is wholly at variance with the truth. Nature itself bears witness that all authority, of every kind, proceeds from God, who is its august and supreme source.
"The sovereignty of the people, which takes no account of God and is said to reside in the natural populace, in itself is a doctrine well calculated to flatter and inflame many passions. Nonetheless it lacks all reasonable proof and all power of insuring public safety and preserving order. Indeed, from the prevalence of this teaching, things have come to pass that many leaders hold as an axiom of civil jurisprudence that sedition may be rightfully fostered. For the opinion prevails that rulers and heads of government are nothing more than delegates chosen to carry out the will of the people. Whence it follows that all things are as changeable as the will of the people, so that risk of public disturbance is ever hanging over our heads" (n. 36).
Religious indifference: "To hold, therefore, that there is no difference in matters of religion among forms that are unlike and even contrary to each other, most clearly leads in the end to the rejection of all religion in both theory and practice. It is Atheism without the name. In effect, whoever believes in God, to be consistent with themselves and not fall into absurd conclusions, must necessarily admit that the diverse cults of worship, among which there is so much difference, disparity, and opposition even on the most important points, cannot all be equally probable, equally good, and equally acceptable to God" (n. 37).
Freedom of thinking and expression: "So, also, liberty of thinking and of publishing whatsoever each one likes without any hindrance is not in itself a good over which society can rejoice. On the contrary, it is the source and origin of many evils. Liberty, that element of perfection for man, should be applied in relation to that which is true and good. However, the essence of goodness and truth cannot be changed at the will of man, but remains ever one and the same, and by the nature of things is immutable. If the mind assents to false opinions, if the will chooses and follows after the evil, then neither the mind nor the will can achieve its perfection. Both fall from their native dignity and are corrupted. Whatever, therefore, is opposed to virtue and truth, may not be permitted to come before the eyes of men to tempt them. And much less can such be sanctioned by the favor and protection of laws" (n. 38).
Excluding the Church from public life: "To exclude the Church, founded by God Himself, from public life, from making laws, from the education of youth, from domestic society, is a grave and pernicious error" (n. 39).
Listening to these wise words of Leo XIII one can hear not only the voice of a great Pontiff but the majestic and grave chorus of multiple past Popes who established the Pontifical Magisterium on this topic. Should someone want to go a step deeper, he might say that the very voice of the Holy Ghost is superbly echoed in these teachings. How can this be proved? If an error could be found in a doctrine the Catholic Church would have taught for many centuries, it would be because the assistance of the Holy Ghost was not constant in the Church. Now then, this assistance was and is constant according to the promise of Our Lord (Mt 28:20; Jn 14:16). Therefore, that doctrine is infallible, by the very fact of being the same throughout the centuries. It is the infallibility granted to the perennial ordinary Pontifical Magisterium.
Therefore, whosoever denies this doctrine rejects the infallible teaching on this matter. In other words, he stops being Catholic.