The following quotes are from older papal documents about the relationship between the Church and the state, and the rights of the Church.
“When we pay honor to the princely dignity of Christ, men will doubtless be reminded that the Church, founded by Christ as a perfect society, has a natural and inalienable right to perfect freedom and immunity from the power of the state; and that in fulfilling the task committed to her by God of teaching, ruling, and guiding to eternal bliss those who belong to the kingdom of Christ, she cannot be subject to any external power.” (Pius XI, Quas Primas 31)
“To wish the Church to be subject to the civil power in the exercise of her duty is a great folly and a sheer injustice. Whenever this is the case, order is disturbed, for things natural are put above things supernatural; the many benefits which the Church, if free to act, would confer on society are either prevented or at least lessened in number; and a way is prepared for enmities and contentions between the two powers, with how evil result to both the issue of events has taught us only too frequently.” (Leo XIII, Immortale Dei 33)
“But, as no society can hold together unless some one be over all, directing all to strive earnestly for the common good, every body politic must have a ruling authority, and this authority, no less than society itself, has its source in nature, and has, consequently, God for its Author. 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, so that whosoever holds the right to govern holds it from one sole and single source, namely, God, the sovereign Ruler of all. ‘There is no power but from God.’” (Leo XIII, Immortale Dei 3)
“Of the rights of the Church that it is Our duty everywhere and always to maintain and defend against all injustice, the first is certainly that of enjoying the full freedom of action she may need in working for the salvation of souls. This is a divine liberty, having as its author the only Son of God, Who by shedding of blood, gave birth to the Church Who established it until the end of time, and chose Himself to be its Head. This liberty is so essential to the Church, a perfect and divine institution, that they who attack this liberty at the same time offend against God and their duty. For as We have elsewhere more than once shown, God established His Church to protect and distribute what is of supreme good to souls, by their nature superior to all others, and to bring men, by means of faith and grace, to a new life in Jesus Christ, a life that ensures eternal salvation.” (Leo XIII, Officio Sanctissimo 13)
“Thus the empire of our Redeemer embraces all men. To use the words of Our immortal predecessor, Pope Leo XIII: ‘His empire includes not only Catholic nations, not only baptized persons who, though of right belonging to the Church, have been led astray by error, or have been cut off from her by schism, but also all those who are outside the Christian faith; so that truly the whole of mankind is subject to the power of Jesus Christ.’[28] Nor is there any difference in this matter between the individual and the family or the State; for all men, whether collectively or individually, are under the dominion of Christ. In him is the salvation of the individual, in him is the salvation of society. ‘Neither is there salvation in any other, for there is no other name under heaven given to men whereby we must be saved.’[29] He is the author of happiness and true prosperity for every man and for every nation. ‘For a nation is happy when its citizens are happy. What else is a nation but a number of men living in concord?’[30] If, therefore, the rulers of nations wish to preserve their authority, to promote and increase the prosperity of their countries, they will not neglect the public duty of reverence and obedience to the rule of Christ. What We said at the beginning of Our Pontificate concerning the decline of public authority, and the lack of respect for the same, is equally true at the present day. ‘With God and Jesus Christ,’ we said, ‘excluded from political life, with authority derived not from God but from man, the very basis of that authority has been taken away, because the chief reason of the distinction between ruler and subject has been eliminated. The result is that human society is tottering to its fall, because it has no longer a secure and solid foundation.’” (Pius XI, Quas Primas 18)

A stained-glass window of Christ the King surrounded by saints in a church in Rome. Photo by Lawrence Lew OP on Flickr under the CC-BY-NC-ND 2.0 license, here.