For the sedevacantists who like to employ this argument, let's put it like this - if the SSPX is in schism, then the sedevacantists certainly are. And if the sedevacantists are not in schism, then the SSPX certainly is not. Sedevacantists do not even recognize there is a Pope to submit to.
Thus, sedevacantists who want to make such an argument will shoot themselves in the foot. On the other hand, dropping the name of the man universally recognized as Pope from the canon, according to Pope Benedict XIV, is an objectively grave act. Sedevacantists live in a glass house and want to throw stones.
This is how the Society has answered this charge - the truth of the matter is that the SSPX is a canonically established society of apostolic life that was illegally suppressed. The possibility of a sentence of suppression being illegal, that is, being unjust or invalidated by an error of fact is taught by St. Thomas, St. Robert, Innocent III among others. Those who receive the unjust sentence must still maintain an attitude of respect toward their superiors, and ask for the decree to be officially rescinded, as in fact the Society has done and is doing.
Innocent III formally admits the possibility of this conflict. Some persons, he says, may be free in the eyes of God but bound in the eyes of the Church; vice versa, some may be free in the eyes of the Church but bound in the eyes of God: for God's judgment is based on the very truth itself, whereas that of the Church is based on arguments and presumptions which are sometimes erroneous.
But all this is unnecessary - on the face of it, as once they implicitly admitted the true Mass was never abrogated while trying for a period of time to maintain otherwise in public, before admitting it expressly, similarly too they now implicitly admit that the Society's apostolate is valid and licit, and will soon admit that expressly.
Then there are painful cases that concern sins so severe they are penalized by excommunication reserved only to the Pope.”
SSPX priests who confront these cases in the confessional absolve the penitent from the sin, and from the excommunication. According to Church policy, the priest must then send the case to Rome to be examined, and the excommunication formally lifted.
Bishop Fellay says, “Every time – absolutely every time – we have received an answer from Rome that the priest who took care of this confession did well, that it was perfectly in order, and it was both licit and valid.” Rome would then comment on the penance, whether it was sufficient or not enough.
In other words, Rome does not say the confession was invalid. Rome accepts the validity of the SSPX confession. Bishop Fellay asks, “So why is it said that our confessions are invalid if this is the way Rome deals with us in the case of these most serious matters?”
Who has ever heard of such a thing - that priests who are supposed to be under suspension can not only absolve validly, but even lift the excommunications of others! With, of course, the necessary notification to the Roman authorities. And this suffices to prove the point, the SSPX is still a legitimately and canonically erected society of the Catholic Church.