So extreme that even Richard John Neuhaus couldn't tolerate them. But he was clear about what they believed in:
Lefebvrists in the Society of St. Pius X are to be found around the world, and have their American headquarters in Kansas City. Some on the right of the party of discontinuity are “sedevacantists” - from sede vacante, meaning “the see is vacant.” They believe John Paul II is an imposter, as was Paul VI before him. They have photos showing that the left ear lobe of Giovanni Battista Montini is very different from the left ear lobe shown in photos of Paul VI, or something like that. In the twilight zones of the Internet, sedevacantism is conveniently linked to websites about Elvis sightings.
Discontinuants of a rightist bent are usually not so radical in their views. They include people who say, sotto voce, that Vatican II was a mistake; some thinking it was a catastrophe, others a wrong turn, and yet others a severe bump in the road.
They say such things sotto voce because the Catholicism they want to repristinate provides no doctrinal resources to justify the claim that Vatican II was simply illegitimate. In their view, the Council was, at the very least, unnecessary. Two councils were quite enough: Trent to definitively rebut the Protestant heretics, and Vatican I to declare papal infallibility, which would then be sufficient for dealing with all future contingencies. John XXIII’s decision to call a council, they believe, was not an inspiration but a wild impulse that a wiser man would have stifled. Discontinuants of the right generally stay in the Church-there being nowhere to go except into the Lefebvre Land of schism-but not without a steady rumble of grumbling.
Of all the people Benedict could have reached out to, these were top of the list. You think that was an accident? You think it doesn't tell us about the kind of church Benedict wants?