The Matthewites are an Old Calendarist Synod, which puts them in a different category from "vaganteism." Occasionally on the internet one hears the idea expressed that vagantes and Old Calendarists are the same but in reality this is not true. Compare www.ind-movement.org
and a good exposition of the Old Calendarist movement and one will immediately see the differences. A few brief points of note would be as poster Serge has often noted, vagantes do not usualy have multi-generational members and real churches as a starter. Vagantes often blend Anglo Catholicism, Orthodoxy, and Catholicism. Vagantes often ordain women and have no theological rigidity. Old Calendarists on the other hand have real Churches, real clergy, multi-generational members, real monasteries, a theology based in Orthodoxy not in amalgamations, etc. The aim of Old Calendarism is to preserve the Orthodox faith in the sight of ecumenism, modernism, etc. Vaganteism has no unified aim.
Now to the specifics. All Old Calendarist groups use the title, "Gnissios" or true in their title because they wished to distinguish themselves from the people who were using the police to beat them, torch their churches, shave their priests and disrobe them, etc. all because they refused to stop using the patristic calendar and submit to the theological innovations of Patriarch Meletios and company. Some posters here will inevitably disagree as to whether these were real issues, big enough issues to separate over, etc. It is not my intent to debate these issues as I already have many times. But instead I simply wish to underscore what provoked these people to begin to use the term Gnissios as a distinguishing term.
The Matthewites' position within Old Calendarism is at the extreme end. They have a light switch view of ecclesiology: 1924, Calendar Change, New Calendarists have no grace. Other Old Calendarists have a much more moderate and nuanced view of the situation. Matthewites will argue they are the only consistent ones but so be it; I'd rather be inconsistent and allow for the obvious fact that there have been holy people in the New Calendar Church post 1924!
The Matthewites are not very large, and in the opinion of many in my Synod (Archbishop Chrysostomos II) they are fanatical and have caused us undue problems. Their break from us (they of course argue the reverse) is what precipitated the divisions in the Old Calendar Church which have made us so unappealing to others and have basically caused us to become stagnant.
Thankfully, instead of trying to woo the Matthewites back to us as we did in the past, we are now more interested in trying to dialogue with the State Church of Greece and effect an end to the Calendar and ecumenism schism rather than becoming ever more insular and parochial. Make no mistake about it--I would not be part of an Old Calendarist synod if I did not believe them to be absolutely right on the doctrinal points--but I believe that the Matthewites and other elements of the Old Calendar movement have done us more harm than good and I am quite willing to be self-critical.
As a down-to-earth example: many New Calendarists see people in the WCC and think "why do they have to do that?!" Many of us Old Calendarists see Matthewites saying all sorts of unseasoned things and think "Why do they have to do that!?"