Traditional Roman Catholic, Independent Catholics, Sedevacantist Catholics, Society of St. Pius X, Society of Pius V, Congregation of Mary Immaculate Queen, etc., the list goes on and on. Since the Roman Catholic Church launched its Second Vatican Council in 1962, several disenchanted Roman Catholics who were less than enthusiastic regarding the changes their Church had made, decided to jump ship and become associated with one or more of the movements listed above. All of the movements above claim to be the real Roman Catholic Church while the Roman Catholic Church as it exists today is some sort of false Church, established by modernists, liberals, freemasons, etc.
The problem with these reactionary groups, from the Society of St. Pius X to the Congregation of Mary Immaculate Queen, is that none of them are Roman Catholic. To be Roman Catholic one must be in communion with the Bishop of Rome, namely the Pope. Now, such pseudo-Roman Catholic groupies, aka, so-called traditional Roman Catholics, are living a fantasy that just is not true. They will claim there is a "state of necessity," "a state of emergency" "an urgency in order to preserve Tradition," etc. They will lay claim to documents of years gone by, centuries gone by, claiming that such decrees from various popes give them the justification for their allegiance to a movement that has separated itself from the Roman Catholic Church in reaction to the Second Vatican Council. Some will quote "Quo Primum" of Pope St. Pius V who 'codified' the Mass for the Roman Church during the Council of Trent. Others will cling to decrees pre-existing the Roman Church's Council of Trent and claim that the Chair of St. Peter becomes vacant when/if a pope should utter heresy....well that could become a very subjective criteria, and in some circles of so-called traditional Roman Catholics, they have fashioned their movement around such archaic decrees that no longer bear authority.
What one pope decrees in one time cannot forever bind a pope that may follow him in a distant future time, especially if such decrees are not a matter of what has been divinely revealed in Sacred Scripture and Sacred Tradition. The Roman Church asserts that the pope bears the authority of loosing and binding, what they interpret to be the Keys of the Office of the Petrine Ministry. If this is in fact true, then popes of every period can loose and bind as time and circumstances determine. The point being that all these so-called traditional Roman Catholic organizations are not Roman Catholic but have separated themselves out from communion with the Roman Catholic Church and are just finding it difficult to accept the fact and reality that their Church has evolved from where she once was during the Council of Trent.
If one makes claim to be a Roman Catholic and member of the Roman Catholic Church then that person must be in communion with the Roman Catholic Church, practicing and embracing the course that the Roman Church has taken and where she finds herself today. To claim to be Roman Catholic and belong to the Roman Catholic Church but following a self designed course that does not correlate to where the Roman Catholic Church is today, is to place oneself outside communion with the Roman Catholic Church.
The Society of St. Pius X, the Society of St. Pius V, the Congregation of Mary Immaculate Queen, the sedevacantists, etc., etc., are not Roman Catholic but have all created separate Churches from the Roman Catholic Church. One can correctly assert that the Society of St. Pius X should properly style itself the Society of St. Pius X Church since that is in fact what it has evolved into, and so on and so forth.
Over the years I have encountered several people who have claimed to have been Roman Catholic, but all they ever knew was one of these pseudo-Roman Catholic organizations; unfortunately, if that was their only exposure to 'Roman Catholicism' then they have not ever experienced the Roman Catholic Church.
If I was an employee of Gateway or IBM and suddenly Gateway or IBM decided to etch a course with their respective company that did not reflect a vision I agreed with, I would resign and move on to something else. Once I resigned and moved on to something else I reasonably would not and could not claim to remain with Gateway or IBM since I would no longer be working with them. I cannot create a separate business and call it 'Gateway' or 'IBM' and pretend to belong to the real Gateway or IBM. Certainly a lawsuit would very quickly follow. If I am no longer working with Gateway or IBM the fact is simple, I am no longer an employee of Gateway or IBM. If I am no longer with the Roman Catholic Church, I cannot claim to be a Roman Catholic just because I have kept the trappings and historical succession. To be a member of the Roman Catholic Church one must belong to the Roman Catholic Church.
In sum, the Society of St. Pius X, the Society of St. Pius V, the Congregation of Mary Immaculate Queen, independent Catholics, sedevacantists are all entitled to be who they are and follow what they want to follow and believe what they want to believe, for this is a matter of conscience. But such should not present themselves to be members of the Roman Catholic Church since they realistically and simply are not.