One must be very very careful with these self-proclaimed Catholic traditional groups, as they lead many astray. And don't be fooled by the beautiful vestments and statues they use and traditional devotions that many of them practice, as they appeal to those who are seeking to find a more sacredly-presented liturgy.
The problem with SSPX is that it was schismatic (disobedient) from the start, and the group has helped spark many of the wickedly deceptive traditional movements around the world, such as the Palmarian Church in Spain whose founder proclaimed himself pope Gregory XVIII, and elsewhere, "Pope Michael" and "Pope Pius XIII" also claim the papal throne, all of whom use the traditional garb, supposedly say the Latin Mass, etc.
These movements begin by ushering people into a hyper criticism of Vatican II which often develops into a repudiation of Vatican II altogether, and in worst cases, morphs into a Sede Vacante position that claims our current Roman Pontiffs are invalid popes. Extreme fanatical groups have led "Traditional Catholics" to elect their own popes.
Below is an extreme example of the Luciferian deceptionand the fruits of disobedience in full bloom. In the video, "Pope Gregory XVIII" has a vision before his flock, a hoax perpetrated by the leader of this Satanic deception. Fast-fowrard the video to 4:55 and see the gloriously beautiful altar, etc. etc. etc.
Note: the Palmarian Catholic Church was founded by Clemente Domínguez, who claimed that the Virgin Mary had given him instructions to rid the Roman Catholic Church of "heresy and progressivism".
So can we lump SSPX with all these groups? In JPII's own words, Archbishop Lefebvre's act "was one of disobedience to the Roman Pontiff in a very grave matter." In Pope John Paul II's Motu Propio ECCLESIA DEI, the pope pleaded, urged and warned Catholics not to support SSPX in any way:
...In the present circumstances I wish especially to make an appeal both solemn and heartfelt, paternal and fraternal, to all those who until now have been linked in various ways to the movement of Archbishop Lefebvre, that they may fulfill the grave duty of remaining united to the Vicar of Christ in the unity of the Catholic Church, and of ceasing their support in any way for that movement. Everyone should be aware that formal adherence to the schism is a grave offense against God and carries the penalty of excommunication decreed by the Church's law...*
"With great affliction the Church has learned of the unlawful episcopal ordination conferred on 30 June last by Archbishop Marcel Lefebvre, which has frustrated all the efforts made during the previous years to ensure the full communion with the Church of the Priestly Fraternity of St. Pius X founded by the same Mons. Lefebvre. These efforts, especially intense during recent months, in which the Apostolic See has shown comprehension to the limits of the possible, were all to no avail."
[ Here is his statement in context]("http://www.vatican.va/holy_father/john_paul_ii/motu_proprio/documents/hf_jp-ii_motu-proprio_02071988_ecclesia-dei_en.html")