They separated themselves from new-rome and the V2 hierarchy, who are not the Church proper, but only Church officials. The Church, the True Bride of Christ, is, as Our Lady of LaSalette said "in eclipse" due to V2 and the new mass, which are themselves schismatic councils and a schismatic mass. There is no obligation for ANY catholic to accept V2 or the new mass under penalty of sin and thus, their ideals are not truly Apostolic nor Traditional.
We're speaking from the perspective of Rome. +ABL severed himself and the SSPX from Rome, which is the Church proper in Xavier's belief. Xavier believes that the Mass and the Council were valid, and that the hierarchy in Rome are valid and the true Church, and therefore he is a schismatic
by his own beliefs.