You mean,
Is Catholicism about to break into three?
Archbishop Viganò: We Are Witnessing Creation of a ‘New Church ’
The SSPX's Relationship with Francis: Is it Traditional? post #6
Is the Catholic Church in De Facto Schism?
The Impossibility of Judging or Deposing a True Pope...If Francis is a true Pope …
Dogmatic Fact: The One Doctrine that Proves Francis Is Pope; https://onepeterfive.com/dogmatic-fact-francis-pope/
A web site popular among “RadTrad” RCs who reject Vatican Two is https://novusordowatch.org and which sums up the situation by saying,
In response to the phenomenon of the Vatican II revolution, there are three essential lines of thought that have been proposed as “solutions” to understanding the situation. This is not now the place or time to critique or justify any of them. For now, we want to just describe them: (1) despite appearances, nothing has really substantially changed, and any interpretation of Vatican II that arrives at the conclusion that there has been a substantial change must be incorrect; (2) we must oppose (resist) these substantial changes and stick to the traditional, age-old teaching instead and ignore the Vatican II novelties while recognizing, however, that the authorities in the Vatican are legitimate and genuine Roman Catholic authorities — we just cannot agree with them on these points; (3) because it is impossible for the Catholic Church to change substantially, and because Vatican II constitutes such an impossible substantial change, it is necessary to conclude that the authority which gave us Vatican II is not in fact the legitimate Catholic authority; that is to say, the “Popes” which gave us Vatican II are not true Popes, nor are their successors, who have implemented and expanded this new religion that has its roots in the council. In fact, the entire religion that now occupies the Vatican and the official structures of the Catholic Church throughout the world is false — it is not the Catholic religion at all, and its putative authorities are not Catholics but heretical usurpers.
The first line of thought described above is often termed (not necessarily correctly) “conservative Catholic”, “orthodox Catholic”, “Novus Ordo”, “conservative Novus Ordo”, or “indult”. Prominent organizations and individuals which can be said to promote or be associated with this position would include Catholic Answers, EWTN, Fraternity of St. Peter, Institute of Christ the King, Franciscan University of Steubenville, National Catholic Register, The Wanderer, Latin Mass Magazine, Church Militant, Vericast, Fr. Kenneth Baker, Rev. John Zuhlsdorf, Karl Keating, Scott Hahn, Michael Voris, Tim Staples, Jimmy Akin, Steve Kellmeyer, Dave Armstrong, Mark Shea, and many others.
The second line of thought described above is often termed (not necessarily correctly) “traditionalist”, “traditional”, “resistance”, “recognize-and-resist” (“R&R”), or “SSPX”. Proponents of this position include the Society of St. Pius X (SSPX), Fatima Network, Tradition In Action, The Remnant, Catholic Family News, TradCatKnight, Bp. Bernard Fellay, Bp. Richard Williamson, Rev. Paul Kramer, Rev. Nicholas Gruner, John Vennari, Michael Matt, Christopher Ferrara, Louie Verrecchio, John Salza, Robert Siscoe, Eric Gajewski, and many more. Here at Novus Ordo Watch we like to refer to this position as “recognize-and-resist”, “neo-traditionalist”, “pseudo-traditionalist”, or “semi-traditionalist”.
The third line of thought is the one we espouse at Novus Ordo Watch, and it is a theological position known as “Sedevacantism”, from the Latin sede vacante, “the chair being empty”, referring to the Chair of St. Peter that is occupied by the Pope — when there is a legitimate Pope reigning. Sedevacantism is by far the least popular position, the “black sheep” no one wants to be “tainted” with. Besides Novus Ordo Watch, other groups or individuals who promote or share this position include True Restoration, the Congregation of Mary Immaculate Queen (CMRI), Istituto Mater Boni Consilii, Sodalitium, Daily Catholic, The Four Marks newspaper, Bp. Geert Stuyver, Bp. Donald Sanborn, Bp. Mark Pivarunas, Bp. Clarence Kelly, Fr. Anthony Cekada, Fr. Michael Oswalt, Fr. William Jenkins, John Daly, Thomas Droleskey, Stephen Heiner, John Lane, Michael Cain, Mario Derksen, Griff Ruby, Steve Speray, and others.
As for the term “Novus Ordo”, in its most general application it simply refers to the new, pseudo-Catholic religion of Vatican II described above.... To be clear: We adhere fully to the Magisterium of the Roman Catholic Church from her founding in 33 A.D. by the Blessed Lord Jesus Christ through the death of the last known Pope, Pius XII, on October 9, 1958. We are Roman Catholics. - https://novusordowatch.org/start-here/
Then we have a more charitable description:
It is certainly possible to discern three tribes within American Catholicism. However, using the Jewish terminology is confusing. “Orthodox,” “Conservative,” and “Reform” do not translate well into American Catholicism. Clearer titles for the three tribes might be “Traditionalist” which correlates with the Jewish “Orthodox.” “Magisterial” because “conservative” Catholics adhere to papal teachings and the magisterium, while “Progressive” reflects the “Reformed” group in Judaism....
Broadly speaking, “Traditionalists” adhere to the Extraordinary Form of the Mass, the Baltimore Catechism, and Church teachings from before the Second Vatican Council...
“Magisterial” Catholics put loyalty to the authority of the pope and magisterial teaching first and foremost. They are happy with the principles of the Second Vatican Council, but want to “Reform the Reform.” They want to celebrate the Novus Ordo Mass with solemnity, reverence, and fine music. ..They uphold traditional Catholic teaching in faith and morals, but wish to communicate and live these truths in an up-to-date and relevant way...
The “Progressives” are vitally interested in peace and justice issues. They’re enthusiastic about serving the marginalized and working for institutional change. They are likely to embrace freer forms of worship, dabble in alternative spiritualities, and be eager to make the Catholic faith relevant and practical. Progressives believe the Church should adapt to the modern age... Maguire sums up their attitude pretty well: Progressives “don’t need the Vatican. Their conscience is their Vatican.” - Is Catholicism about to break into three? Crux Catholic Media Inc. ^ | Oct 6, 2015 | Fr. Dwight Longenecker; http://www.freerepublic.com/focus/f-religion/3778496/posts
If one church, Catholicism is an unholy amalgamation of liberals and conservatives, and of conflicting interpretations of what valid church teaching is and means, and far less unified in than those who most strongly esteem Scripture as the accurate and wholly inspired word of God, which Catholics attack as a basis for unity.