The SSPX is often referred to in the secular media as an “ultra-traditionalist” or “extremist” body. This risks exhausting the adjectives needed to describe the many groups who self-identify as Catholic. For one thing, the SSPX has itself been divided. Some members have decided that submission to Rome is a sine qua non, and formed societies that preserve traditional liturgy while reconciling with the Vatican. Others have left the SSPX, feeling that it has compromised too far with modernity.

The most recent case is the “SSPX Resistance”, which broke away when a Vatican deal seemed near under Benedict XVI. It is led by Bishop Richard Williamson, whose views on the Holocaust led him to be convicted of “incitement to hatred” by a German court. Bishop Williamson has consecrated two new bishops, confirming the Resistance’s separation from the SSPX.

The story of SSPX breakaway groups is, for critics of the SSPX, a cautionary tale about what happens when you separate from Rome. Not only have the new bodies themselves divided – the Society of St Pius V, for instance, had an internal schism a few years after leaving the SSPX – they have often ventured down the path of sedevacantism. For some ultra-traditionalists, there have been no genuine popes since Pius XII, since the rest, by teaching error, forfeited their office. Others, called sedeprivationists, hold a complex position about modern pontiffs being only “potentially” pope.

The blogger Fr John Hunwicke argues that these positions are overreactions to another error – the belief that whatever a pope says, even in interviews and letters, must be correct. While one group appears to think, “The pope always speaks with total authority – therefore, we must always agree with him about everything,” the other group thinks, “The pope always speaks with total authority – therefore, since he has been wrong, he can’t be pope.” Both errors, Fr Hunwicke writes, are “equally dangerous to souls”.

Sedevacantism’s best-known advocate is probably Hutton Gibson, though mostly because of his film-maker son. Mel Gibson’s own views are not clear – some have described him as a sedeprivationist – but he finances the Church of the Most Holy Family in California, where various ultra-traditionalists, some of them sedevacantists, worship.

What makes people adopt ultra-traditionalist positions? A frequent reason is a fear that the doctrine of “no salvation outside the Church” has been abandoned. One website, for instance, claims that the SSPX is heretical because its leader, Bishop Bernard Fellay, has supposedly said that “a Hindu in Tibet who has no knowledge of the Catholic Church” could, under some circumstances, go to heaven.

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