Problem: If the official apparatus is not Catholic and not to be obeyed, then where is the Catholic Church ? All theologians and canonists prior to the Council speak in terms of "profession of Faith" as a prerequisite for membership in the church, but unity of government is also essential, i.e. submission to the Roman Pontiff and the Catholic bishops in communion with him. Thus two essential credentials must be established: what Faith is professed (what do they believe) and are they in union with the Roman Pontiff ?
The Authority of the Church by Saint Francis de Sales (1567-1622), Bishop and Doctor of the Church
http://www.catholicapologetics.info/apologetics/protestantism/authorityds.htm(Below is Chapter IV - Unity of the Church
OF THE UNITY OF THE CHURCH IN DOCTRINE AND BELIEF. THE TRUE CHURCH MUST BE ONE IN ITS DOCTRINE. THE CATHOLIC CHURCH IS UNITED IN BELIEF, THE SO CALLED REFORMED CHURCH IS NOT.
Is Jesus Christ divided? No, surely, for he is the God of peace, not of dissension, as S. Paul taught throughout the Church. It cannot then be that the true Church should be in dissension or division of belief and opinion, for God would no longer be its Author or Spouse, and, like a kingdom divided against itself, it would be brought to desolation. As soon as God takes a people to himself, as he has done the Church, he gives it unity of heart and of path the Church is but one body, of which all the faithful are members, compacted and united together by all its joints; there is but one spirit animating this body: God is in his holy place: who maketh men of one manner to dwell in a house (Ps. ixvii. 7); therefore the true Church of God must be united, fastened and joined together in one same doctrine and belief.
It is necessary, says S. Irenmus (iii. 3) that all the faithful should come together and unite themselves to the Roman Church [on account of] its superior ruling power. She is the mother of their sacerdotal dignity, says Julius I. (ad Euseb.) "She is the commencement of the unity of the priesthood, she is the bond of unity," says S. Cyprian (Ep. 5 5). Again: "We are not ignorant that there is but one God, one Christ and Lord, whom we have confessed, one Holy Spirit, one pastoral office (episcopatus) in the Catholic Church " (de un. Ec. iv.). The good Optatus also said to the Donatists (ii. 2, 3) : " Thou canst not deny that thou knowest that in the city of Rome the chief chair has been first granted to S. Peter, in which sat the chief of the Apostles, S. Peter, whence he was called Cephas ; the chair in which the unity of the whole was preserved, in order that the other Apostles might not seek to put forward and maintain each his own, and that henceforward he might be a schismatic who would set up another chair against this one chair. Therefore in this one chair, which is the first of its prerogatives, was first seated S. Peter." These are almost the words of this ancient and holy doctor; and every Catholic of this age is of the same conviction. We hold the Roman Church to be our refuge in all our difficulties; we all are her humble children, and receive our food from the milk of her breasts; we are all branches of this most fruitful stock, and draw no sap of doctrine save from this root. This is what clothes us all with the same livery of belief; for knowing that there is one chief and lieutenant general in the Church, what he decides and determines with the other prelates of the Church when he is seated in the chair of Peter to teach Christendom, serves as law and measure to our belief. Let there be error everywhere throughout the world, yet you will see the same faith in Catholics. And if there be any difference of opinion, either it will not be in things belonging to the faith, or else, as soon as ever a General Council or the Roman See shall have determined it, you will see every one submit to their decision. Our understandings do not stray away from one another in their belief, but keep most closely united and linked together by the bond of the superior authority of the Church, to which each one gives in with all humility, steadying his faith thereon, as upon the pillar and ground of truth. Our Catholic Church has but one language and one same form of words throughout the whole earth. Letter of Saint Athanasius to His Flockhttp://www.olrl.org/snt_docs/athnasus.shtml"May God console you! ... What saddens you ... is the fact that others have occupied the churches by violence, while during this time you are on the outside. It is a fact that they have the premises – but you have the Apostolic Faith. They can occupy our churches, but they are outside the true Faith. You remain outside the places of worship, but the Faith dwells within you. Let us consider: what is more important, the place or the Faith? The true Faith, obviously. Who has lost and who has won in the struggle – the one who keeps the premises or the one who keeps the Faith? True, the premises are good when the Apostolic Faith is preached there; they are holy if everything takes place there in a holy way ...
"You are the ones who are happy; you who remain within the Church by your Faith, who hold firmly to the foundations of the Faith which has come down to you from Apostolic Tradition. And if an execrable jealousy has tried to shake it on a number of occasions, it has not succeeded. They are the ones who have broken away from it in the present crisis. No one, ever, will prevail against your Faith, beloved Brothers. And we believe that God will give us our churches back some day.
"Thus, the more violently they try to occupy the places of worship, the more they separate themselves from the Church. They claim that they represent the Church; but in reality, they are the ones who are expelling themselves from it and going astray. Even if Catholics faithful to Tradition are reduced to a handful, they are the ones who are the true Church of Jesus Christ." St. Athanasius