The Society of St. Pius X has always recognized and adhered to the authority of the pope, and, as noted by prominent Roman authorities (e.g., Cardinal Castrillon Hoyos), the SSPX is not schismatic.
A first argument to this is given under the heading: Wasn't Archbishop Lefebvre Excommunicated?
What, moreover, constitutes a schismatic act? Not the mere deed of consecrating bishops without pontifical mandate. The 1983 Code of Canon Law itself lists this offense under Title 3 (abuse of ecclesiastical powers) and not under Title 1 (offenses against religion and the unity of the Church) of its penal section (Book 6).
Nor would it be a “schismatic act” to consecrate against the express wish of the Holy Father. That could amount to disobedience at most.* But disobedience does not amount to schism; schism requires that one not recognize the authority of the pope to command; disobedience consists in not obeying a command, whilst still acknowledging the authority of the one commanding. “The child who says ‘I won’t!’ to his mother does not deny that she is his mother” (Fr. Glover, in Is Tradition Excommunicated? p. 99 [appendix 2]).
*(But there is no disobedience, cf. An Open Letter to Confused Catholics, pp. 129-136. Cf. "The act of consecrating a bishop (without the pope's permission)is not itself a schismatic act," Cardinal Lara, President of the Pontifical Commission for the Authentic Interpretation of Canon Law, in La Repubblica, October 7, 1988)
Archbishop Lefebvre always recognized the pope’s authority (proved by his consultations with Rome for a solution to the current problems) and so does the SSPX. (See for example, its support for Pope John Paul II’s Ordinatio Sacerdotalis against women priests.)
Consecrating a bishop without pontifical mandate would be a schismatic act if one pretended to confer not just the fullness of the priesthood but also jurisdiction, a governing power over a particular flock. Only the pope, who has universal jurisdiction over the whole Church, can appoint a pastor to a flock and empower him to govern it. But Archbishop Lefebvre never presumed to confer anything but the full priestly powers of holy orders, and in no way did he grant any jurisdiction (which he himself did not have personally to give).
Not at all. The priests of the Society are neither excommunicated nor schismatics (as figures such as Cardinal Hoyos have made clear) that the Society is not schismatic (Is Tradition Excommunicated? pp. 1-39). This being so, how could any of the faithful who approach them incur these penalties?
On May 1, 1991, Bishop Ferrario of Hawaii “excommunicated” certain Catholics of his diocese for attending Masses celebrated by priests of the SSPX, and receiving a bishop of the Society to confer the sacrament of Confirmation. Cardinal Ratzinger, Prefect of the Congregation for the Doctrine of the Faith, overturned this decision:
From the examination of the case... it did not result that the facts referred to in the above-mentioned decree, are formal schismatic acts in the strict sense, as they do not constitute the offense of schism; and therefore the Congregation holds that the decree of May 1, 1991, lacks foundation and hence validity." (June 28, 1993)
Get the book: Most Asked Questions about the SSPX>