Note: I think by now most HoFers are aware of my cold, seething hatred of anti-semitism. I find Williamson contemptible and in no way may my comments be construed as defending the miserable SOB
The Society or Confraternity of St Pius X was formed in 1970 by the ultraconservative French archbishop Marcel Lefebvre. Although chartered under the auspices of the Bishop of Lausanne, the SSPX was denied worldwide status several times by the Vatican. The premise of Lefebvre and his followers was that the reforms of the Second Vatican Council were illegitimate, and violated in particular the old Catalogue of Abominations and attendant "Oath Against Modernism," which anathematized such ideas as democracy and freedom of religion. When Lefebvre went so far as, in 1975, to issue a "Declaration" condemning the Council and all its works, the Roman curia called him in for denunciation; the See of Lausanne withdrew the SSPX's pia unio status. From then on the SSPX had no recognised existence, and its right-wing seminary, though not closed, was forbidden to ordain priests.
In 1976 Lefebvre brazenly ordained two SSPX priests anyway, and was immediately stripped of his right to perform any of the Sacraments whatsoever- making him, in functional effect, not just a non-bishop but a non-priest.
However (and this is important): under Church law, the ordination of a Bishop is permanent and for life. The Vatican can strip a bishop's authority, but not his title, and spiritually, cannot remove him from the apostolic succession.
The final break came in 1988, when the 81-year-old Lefebvre attempted to create a succession for his unrecognized Society by announcing his intention of consecrating four bishops of his own making. This violated not only his suspension a divinis, but the rule that no bishop may be consecrated without the Pope's approval. Lefebvre was warned by then-Cardinal Ratzinger to desist on pain of excommunication; the archbishop went ahead and he was formally excluded from the Church, together with his four new bishops.
Here, however, the tricksy details of theology arise. While Lefebvre was under a ban on performing any sacraments, including consecration, and violated both the rule of Papal assent and a direct Papal order to desist- none of those violations are considered to affect his power to create bishops- merely his right to do so.* Although the consecrations were "sacriligious, illicit, and criminal," the four priests in question were nonetheless bishops- although excommunicate and forbidden all association with the Faithful.
Point to note here: the excommunications were not based on the political views of any of the participants, but on the illegal and disobedient act of schismatic consecration.
Many members of the SSPX recanted, disavowed Lefebvre, and joined very conservative but legal groups such as the Priestly Fraternity of St Peter and the Society of the Good Shepherd. Others, however, left to join extremist (and outlawed) factions such as the Society of St Pius V, which regards John XXIII and his successors as false anti-popes.
Since Lefebvre's death, the Church has had a policy of trying to heal the schism- but only on its own terms, namely that the Pope is the Boss, the 2nd Vatican Council authoritative, and that the schismatics return to obedience. This, finally, the four SSPX bishops did, and accordingly were readmitted to membership in the Church.
Unfortunately, the press has been caught up with the idea that these four have been "rehabilitated;" -and, even worse, implied that the excommunication and its lfting were connected in some way to Williamson's odious opinions, or generally to the SSPX's reactionary political views (e.g. strong support for LePen's National Front). This distorts and confuses the matter. The four bishops have not been 'rehabilitated'- i.e., given an apostolic mission- and it's unlikely in the extreme that Williamson ever will be, unless he makes an abject recantation. *All* that has happened to date is that the four may now attend Mass and receive communion in legitimate churches.
Lost in all the uproar has been the fact that the Church, long ago, denounced Holocaust denial in the strongest possible terms, and holds anti-semitism to be a grave sin.The Secretariat of State wrote:While the lifting of the excommunication freed the four bishops from a very grave canonical penalty, ... the four bishops remain without any canonical function in the Church and are not exercising legitimately any ministry within it.
However, sin is not grounds for excommunication- since if that were the case, all people being sinners, there would be no Church.
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* If this is hard to wrap your head around, consider this: it's unlawful (according to the Church) to engage in extramarital sex- but if such intercourse results in offspring, the child is still a child. While the parents have no legal right to make a baby, they certainly have the power to do so.