A taxonomy of traditionalism

For those who are new to traditional Catholicism, the various different groups can be hard to understand and clearly distinguish.  I haven’t seen a succinct summary of the different varieties of traditionalist, so I will attempt to summarize here.  But first, let me begin with a definition.  What is a traditionalist Catholic?  A traditionalist Catholic is a Catholic who rejects, in some way, the changes which happened in the Catholic Church as a result of the Second Vatican Council.  As we will see, this covers a broad spectrum.  Most Catholics do not consider a “traditional” Catholic to be the same as a “conservative” Catholic.  While anybody in the traditionalist milieu would be considered “conservative” by the standards of the modern world, when we refer to conservative Catholics we usually mean Catholics who are not particularly concerned with Vatican II or modernism, and probably even accept both of them.
Indult Traditionalists:  So-called because they first showed up when John Paul II issued an indult permitting the Latin Mass under his motu proprio Ecclesia Dei.  These Catholics operate fully within the approved Church structure.  Some are utterly opposed to the new Mass and the new Church in general, while others will quite freely go to Novus Ordo masses as long as they are “reverent.”  Generally these Catholics accept the Vatican II documents, but believe they have been hijacked and misinterpreted by liberal modernists.  Indult traditionalist groups include the Priestly Fraternity of St. Peter (FSSP), Institute of Christ the King Sovereign Priest (ICRSS), and various diocesan priests who say the traditional Mass.  Some of these diocesan priests continue to say the New Mass, while some will exclusively say the TLM.
Recognize and Resist:  R&R Catholics recognize the current pope as valid, but they believe he is evil and possibly a heretic.  They therefore recognize him in name only and tend to ignore most attempts by the pope to use his authority.  They reject Vatican II as a heretical council that is not consistent with Catholic tradition.  The most notable of these groups is the Society of St. Pius X (SSPX), although there are a number of other groups as well.  Tradition in Action is another example of such a group, and they are not supporters of SSPX even though they espouse similar positions.
Resignationist:  Resignationists believe that Pope Benedict XVI was a valid pope, but that Pope Francis is not.  They believe that Benedict’s resignation was invalid for some reason, and that he therefore continues to be pope.
Sedevacantist:  Sedevacantists (from the Latin meaning “empty chair”) believe that the current pope is not, in fact, pope at all, but a false claimant to the title.  They believe that the See of Peter became vacant sometime around Vatican II.  I’ve heard different accounts of who was the last real pope, but it is usually either John XXIII or Paul VI.  All popes since then are false popes.  Although it is not directly part of the sedevacantist thesis, normally sedes believe that the new rite of episcopal consecration, and probably the new rite of ordination, are invalid.  Therefore, any bishop consecrated (or priest ordained) in the new order is not truly a bishop (or priest).  This means that not only the pope, but most of the hierarchy, are imposters as well.  There are several sub-divisions of sedevacantism.  Father Anthony Cekada is probably the most articulate spokesman for this thesis, although there are several groups (e.g., Most Holy Family Monastery) that do not agree with his positions. Conclavist:  Conclavists are sedevacantists who believe that it is necessary to elect a new pope since the Holy See is vacant.  They believe they are a tiny remnant of true Catholicism, and therefore have a right to proceed with their own election.  Pope Michael is the most prominent example.  They generally have a very small following.