What about “material/formal pope sedevacantism” (Cassiciacum Thesis)?

THE ABOVE VIDEO IS VERY IMPORTANT AND REFUTES THE CASSICIACUM THESIS

Steven, you are referring to the Cassiciacum Thesis or the “material/formal pope” idea.  It is not actual sedevacantism.  It's the theory that the Vatican II claimants to the Papacy have valid elections, but not jurisdiction over the Church.  Adherents of this idea also hold that the Vatican II Sect is not an entity different from the true Church and that all members of the Novus Ordo (who have not been declared heretics) are Catholics!  They make many anti-sedevacantist arguments to defend their false position.

The thesis also holds that the Vatican II antipopes receive jurisdiction to appoint cardinals, and that the apostate 'cardinals' of the Vatican II Sect are true cardinals.  The thesis is false, and amounts to a position half-way between the position of the SSPX and actual sedevacantism.  If a man is a pope, he has full and supreme jurisdiction over the Church.  If not, then he lacks jurisdiction proper to the office.  Also, heretics cannot be validly elected pope.

Pope Pius IX, Vatican I, 1870, Sess. 4, Chap. 3, ex cathedra: “If anyone thus speaks, that the Roman Pontiff has only the office of inspection or direction, but not the full and supreme power of jurisdiction over the universal Church… let him be anathema.” (Denz. 1831)

The proposition anathematized above, especially the bolded portion, is what many 'recognize and resist' false traditionalists have fallen into.  A true pope cannot be separated from his authority.  But if a man is not a true pope, then he does not have jurisdiction proper to the papal office.  The Vatican II claimants to the Papacy are heretics.  Since they are outside the Church, they have no jurisdiction.  The Cassiciacum Thesis must be rejected.  The main adherents of the Cassiciacum Thesis in our day are the members of Bishop Donald Sanborn's group, who also deny the Catholic faith by professing that members of false religions can be saved without the Catholic faith.

I also want to mention something that really bothers us. The SSPX recently published a book called Sedevacantism: A False Solution to a Real Problem. This heretical book was actually advertised by the apostate John Vennari in Catholic Family News. The entire first portion of this book deals with the material/formal pope idea, which is not full and consistent Sedevacantism (even though it claims to be). So, get this: the incredibly dishonest SSPX publishes a book supposedly addressing the question of Sedevacantism, when most of the first portion of the book deals with a position that isn’t even straightforward Sedevacantism. This enables the SSPX to deceive their readers again, by making it appear as if they are addressing the main arguments for Sedevacantism when the fact is they are not. This is how heretics kill souls and lead them astray.