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Conciliar Church is a rhetorical device. We say Cardinal Sarah represents the Catholic Church while Kasper et al represent the Conciliar Church. It is not to be misunderstood that the Conciliar Church is like, for e.g. the Orthodox Churches, or the Protestant communities.

Anyone who thinks the Pope and the Bishops appointed by him, are not in general the Catholic Church, but some "Conciliar Church", are just using terms wrongly. It reminds me of Orthodox calling the Catholic Church, "the Papal Church", of Old Catholics calling the Catholic Church, "the Infallibilist Church", of some people who were opposed to mistakes made in negotiating Concordats, "The Concordatist Church" and so on. Read the Catechism of His Holiness Pope St. Pius X and you will see what the Catholic Church is and how you identify Her. Although written a century ago, the same means the Holy Father wrote of then can still be used to identify the Church today.

This is Rev. Fr. Jean Michel Gleize, Seminary Professor of Ecclesiology at Econe: https://fsspx.news/en/content/23744

"Eleventh, Bishop Fellay9 recently stated that the contemporary Church, as represented by the Roman authorities, remains the true Church, one, Catholic, holy, and apostolic. “When we say extra Ecclesiam nulla salus, out of the Church, no salvation, it is indeed to the Church of today that we refer. That fact is absolutely certain. We must cling to it. […} Going to Rome does not mean we agree with them. But Rome is the Church, and the true Church10.” He speaks further of “the Church, which is not an idea, which is real, which stands before us, which we call the Roman Catholic Church, the Church, with its pope, its bishops, debilitated as they may be ... 

The emphasis on the concrete reality of the contemporary Church is only intended to show that in spite of everything, the Church holds the promise of eternal salvation. “In rejecting what is wrong, we must not reject everything. The Church remains one, holy, Catholic and apostolic. […] When we reject the evil found in the Church, we must not conclude that it is no longer the Church. Large parts of it are no longer the Church, true. But not all of it ... And the same dual concept is expressed in the metaphor of an invalid, as used by Bishop Fellay at the last Congress of Courrier de Rome: “The Catholic Church is our Church. We have no other. There is no other. The Good God has allowed it to become diseased. For this reason we try to avoid contagion ourselves. But for all that we are not trying to form another Church. […] The disease is a disease; it is not the Church itself. It is within the Church, but the Church remains itself. […] Certainly, we must fight the disease. But this diseased Church is indeed the Church founded by Our Lord. It alone holds the promise of eternal life. To it alone has been promised that the gates of hell will not prevail42.” We can therefore speak of a ‘conciliar Church’, in order to indicate that among the leaders of the Church and among many of its faithful there is an orientation or a spirit that are foreign to the Church and obstruct its good. (Courrier de Rome B.P 10158 – 78001 Versailles Cedex – Fax 01 49 62 85 91 – Email: courrierderome@wanadoo.fr)"

XavierSem must have skimmed over Sean's post on page 1 of this thread:

From the Dominicans of Avrille (http://www.dominicansavrille.us/is-there-a-conciliar-church/):

To affirm that the official church is the Catholic Church, – something which Archbishop Lefebvre never did – leads one to look for an official recognition, because one cannot remain outside of the Catholic Church. With his new manner of speaking, this is exactly what Bishop Fellay is trying to persuade the priests and faithful to do, and that puts Tradition in grave danger.

So Ladislaus certainly has a point in accusing XavierSem of schism.  He is neither consistent with Archbishop Lefebvre nor with his hero Burke.  As Archbishop Lefebvre used to say, to the extent that you adhere to the Conciliar Church, you separate yourself from the Catholic Church.  The only ones denying the existence of the Conciliar Church are those who desire to pass it off as the Catholic Church.

Conciliar Church is a rhetorical device. We say Cardinal Sarah represents the Catholic Church while Kasper et al represent the Conciliar Church. It is not to be misunderstood that the Conciliar Church is like, for e.g. the Orthodox Churches, or the Protestant communities.

Anyone who thinks the Pope and the Bishops appointed by him, are not in general the Catholic Church, but some "Conciliar Church", are just using terms wrongly. It reminds me of Orthodox calling the Catholic Church, "the Papal Church", of Old Catholics calling the Catholic Church, "the Infallibilist Church", of some people who were opposed to mistakes made in negotiating Concordats, "The Concordatist Church" and so on. Read the Catechism of His Holiness Pope St. Pius X and you will see what the Catholic Church is and how you identify Her. Although written a century ago, the same means the Holy Father wrote of then can still be used to identify the Church today.

This is Rev. Fr. Jean Michel Gleize, Seminary Professor of Ecclesiology at Econe: https://fsspx.news/en/content/23744

"Eleventh, Bishop Fellay9 recently stated that the contemporary Church, as represented by the Roman authorities, remains the true Church, one, Catholic, holy, and apostolic. “When we say extra Ecclesiam nulla salus, out of the Church, no salvation, it is indeed to the Church of today that we refer. That fact is absolutely certain. We must cling to it. […} Going to Rome does not mean we agree with them. But Rome is the Church, and the true Church10.” He speaks further of “the Church, which is not an idea, which is real, which stands before us, which we call the Roman Catholic Church, the Church, with its pope, its bishops, debilitated as they may be ...

The emphasis on the concrete reality of the contemporary Church is only intended to show that in spite of everything, the Church holds the promise of eternal salvation. “In rejecting what is wrong, we must not reject everything. The Church remains one, holy, Catholic and apostolic. […] When we reject the evil found in the Church, we must not conclude that it is no longer the Church. Large parts of it are no longer the Church, true. But not all of it ... And the same dual concept is expressed in the metaphor of an invalid, as used by Bishop Fellay at the last Congress of Courrier de Rome: “The Catholic Church is our Church. We have no other. There is no other. The Good God has allowed it to become diseased. For this reason we try to avoid contagion ourselves. But for all that we are not trying to form another Church. […] The disease is a disease; it is not the Church itself. It is within the Church, but the Church remains itself. […] Certainly, we must fight the disease. But this diseased Church is indeed the Church founded by Our Lord. It alone holds the promise of eternal life. To it alone has been promised that the gates of hell will not prevail42.” We can therefore speak of a ‘conciliar Church’, in order to indicate that among the leaders of the Church and among many of its faithful there is an orientation or a spirit that are foreign to the Church and obstruct its good. (Courrier de Rome B.P 10158 – 78001 Versailles Cedex – Fax 01 49 62 85 91 – Email: courrierderome@wanadoo.fr)"

It was against the position of Fr. Gleize that Bishop Tissier wrote the article I posted on P.1 of this thread.

As for Bishop Fellay, he believes the "official" (i.e., conciliar) church = the Catholic Church.

This is because, as a means to achieving his ralliement, he must do away with distinguishing in any substantive manner between the conciliar and Catholic Church: How could he explain joining the former when Archbishop Lefebvre so famously stressed the duty to remain separate from it?

In this regard, Bishop Fellay utterly rejects Archbishop Lefebvre, and multiple priests could testify that in the retreats Bishop Fellay preaches to priests, in the reading of Spiritual Journey, Bishop Fellay skips right over the famous command of Lefebvre that “It is, therefore, a strict duty for every priest wanting to remain Catholic to separate himself from this Conciliar Church for as long as it does not rediscover the tradition of the Church and of the Catholic Faith.” (Abp. Lefebvre, Spiritual Journey, p. 13).

Bishop Fellay is a traitor, and he knows it.

That's why he skips that passage in the retreats he preaches to priests:

He doesn't want them to perceive the contradiction between Lefebvre and himself.

And they, for the most part, don't read Lefebvre anyway (at least not his polemical works: They are semi-conscious that it is a thought-crime, and steer clear of him), so the "oversight" passes without a glitch; perhaps a momentary discomfort, until CRIMETHINK smothers any remaining tremors of cognitve dissonance.

XS is giving you neo-SSPX doctrine (contradicted by 40 years testimony to the contrary).