Just a note of clarification--the group in question here is not any part of the three major branches of the Franciscan Order, which are OFM, OFM (Cap) and OFM (Conv).
While all Franciscans are devoted to Mary (and the Conventual Franciscans in particular are devoted to the Immaculate Conception thanks to St. Maximilian Kolbe), this title "Franciscans of the Immaculate" is completely new to me.
Now that I've read the second link, this is clearer:
The two orders - The Franciscan Friars of the Immaculate and the Franciscan Sisters of the Immaculate - have interesting histories. The friars were founded in 1970 and the sisters some years later.
I doubt that these two "orders" have more than a few hundred members between them, which would hardly make them "the largest Latin traditionalist order in the world."
(BTW, the term "order" in the RCC technically refers only to groups established
before the Council of Trent--the Jesuits just barely made the cut!)
The Franciscan Friars of the Immaculate began as a reform movement in the OFM Conventuals in 1970, led by Stefano Manelli OFMCOnv. In the 1970's, this reform movement was given jurisdiction over the nascent OFM Conventual Custody in the Philippines, which accounts for the fact that next to the Italians, it is the Filipinos who form the second largest contingent of friars in the present FFI.
By the late 1980's, controversy over the reform movement's strict austerities (use of the hairshirt and discipline and other intense corporal penances, cropped hair, use of the habit at all times, contemplative practices) and its supposedly "excessive" Marian devotion led to a formal split, with many Italian and most Filipino friars leaving the OFMConv and joining the new FFI. It is my understanding that many Conventual Franciscans saw the reformists' emphasis on the spirituality of St. Maximilian Kolbe -- itself based strongly upon the "Marian slavery" spirituality of St. Louis Marie Grignion de Montfort -- as being excessive and un-Franciscan. The FFI, sees itself as simply amplifying the Marian devotion that has always been central to Franciscan identity. However, it is true that the FFI treats St. Maximilian Kolbe as almost a second father, alongside St. Francis.
The FFI was approved in 1998 as being of Pontifical Right. Since the FFI follows the Regula Bullata or 1223 Rule of St. Francis, the FFI is considered as a true Order, and as part of the Franciscan family, although the FFI does not yet have the same privileges and rights as the "Big Three" of the Franciscan First Order -- Conventuals (OFMConv), Capuchins (OFMCap), and the Observantines or Friars of the Leonine Union (OFM). Furthermore, the nuns of the FFI are unique in that they are the only nuns in the world who are considered as part of the Franciscan First Order, since they follow the 1223 Rule of the friars. (The Poor Clares are Second Order, while the various Franciscan sisterhoods are Third Order)
The FFI will now be the largest congregation dedicated to the TLM or the Missal of 1962, unless the SSPX is counted (the SSPX has nearly 500 priests). The FFI has some 300 friars. The FSSP would now be the second largest: it currently has 174 priests as well as some 34 priests who are either associates or postulants. The ICRSP has about 50 priests. The Apostolic Administration in Brazil (not exactly a congregation, but the only "TLM" diocese in the whole world) has, I believe, around 40 priests. All other religious congregations dedicated to the TLM are actually quite small (e.g. Canons of the Mother of God have 30 monks, the 8 monasteries of Trad Benedictines in communion with Rome have a couple of hundred monks all in all, the Trappists of Mariawald have 14 monks)
Of course... they are all growing fast!
My knowledge of the FFI - OFMConv split is based on personal conversations with friars from both groups, especially those who had lived through the actual split in 1989, which was very traumatic in the Philippines and which saw Filipino bishops and the Cardinals of Cebu and Manila take different sides: the late Cardinal Sin of Manila supported the OFMConv and restricted the FFI, while Cardinal Vidal of Cebu gave refuge to the FFI.
