Two birds of one feather?
Rorate Caeli is reporting an eye-witness rumor of the following:
"There will be no return to Rome. The Superior of the Lefebvrians for Spain and Portugal, [Fr.] Juan María Montagut, will inform the faithful, after the 11 AM Mass, that the hierarchy of the SSPX, assembled in Écône, has decided to say "no" to the Vatican.
The followers of [Abp.] Marcel Lefebvre do not return to the Roman fold. Mainly because they are not willing to accept the Second Vatican Council in all its farthermost points.
The Vatican, by way of the [then] Prefect for the Doctrinal of the Faith, Cardinal Levada, had asked from them "the full acceptance of the Council". And the Lefebvrians are not willing to return under this condition. They believe that accepting the Council would imply accepting its errors that, according to them, are particularly centered in the chapters on "religious liberty, ecumenism, and conciliarism" [? - Collegiality?...]"
Thus by rejecting the Supreme Pastor's (Pontiff's) initiatives to bring this group back into the full communion of the truth of the true Church and true faith, have they thus reiterated their "false religion" status?
It is very serious for any Catholic or group of Catholics to reject the authority of the pope in the areas of faith, morals, and canon law (Church discipline) and to do so indicates that such people or groups of people do not have the fullness of truth when it comes to the true religion, causing them to form their own "false" religion no matter how much or how little of the truth they have--like Protestants, they become neo-Protestants, thus a "false" religion.
To reject the authority of the popes and an Ecumenical Council also seems to be a decision for schism similar to the Old Catholics just after Vatican I and its definition of Papal Infallibility.
Wikipedia's definition of Old Catholics certainly can be applied to the SSPX:
The term Old Catholic Church is commonly used to describe a number of Ultrajectine Christian churches that originated from Catholics after the Pope declared certain doctrines within the Roman Church. The Old Catholic Church remained faithful to the original teachings of the Church and the Roman Church split from the Old Catholic Church over certain doctrines, most importantly that of Papal Infallibility. These churches are not in communion with the Holy See of Rome, but their Union of Utrecht of Old Catholic Churches is in full communion with the Anglican Communion and a member of the World Council of Churches. The formation of the Old Catholic communion of Germans, Austrians and Swiss began in 1870 at a public meeting held in Nuremberg under the leadership of A. Döllinger, following the First Vatican Council. Four years later episcopal succession was established with the ordination of an Old Catholic German bishop by a prelate of the Church of Utrecht. In line with the "Declaration of Utrecht" of 1889, they accept the first seven ecumenical councils and doctrine formulated before 1054, but reject communion with the pope and a number of other Roman Catholic doctrines and practices. The Oxford Dictionary of the Christian Church notes that since 1925 they have recognized Anglican ordinations, that they have full communion with the Church of England since 1932 and have taken part in the ordination of Anglican bishops.
The term "Old Catholic" was first used in 1853 to describe the members of the See of Utrecht who did not recognize any claimed "infallible" papal authority. Later Catholics who disagreed with the doctrine of Papal Infallibility as made official by the First Vatican Council (1870) had no bishop and so joined with Utrecht to form the Union of Utrecht.