A significant but unpublished fraction.
The SSPX chose to continue to follow a man formally Excommunicated. and then to Elect another excommunicated in the same bull to replace him as the Superior General of their society.
The SSPX had no such situation. From where I sit, the whole SSPX should be excommunicated formally (mind you, there technically are no laymen in the SSPX, as they are a clerical fraternity) for disobedience and breaking canon law. But since, by voting for Felley, and accepting Fellay as superior General, they engaged in direct violations of canon law, and thus have excommunicated themselves, too.
I can understand why they are not formally excommunicated,
It is my understanding that there never was a formal excommunication. By his disobedience Archbishop Lefebvre excommunicated himself. However he believed that the Church was in a time of crises and it was his duty to consecrate the Bishops. He believed that the following canons allowed him do this.
Can. 1323 The following are not subject to a penalty when they have violated a law or precept:
/ a person who acted coerced by grave fear, even if only relatively grave, or due to necessity or grave inconvenience unless the act is intrinsically evil or tends to the harm of souls;
Can. 1324 §1. The perpetrator of a violation is not exempt from a penalty, but the penalty established by law or precept must be tempered or a penance employed in its place if the delict was committed:
/ by a person who was coerced by grave fear, even if only relatively grave, or due to necessity or grave inconvenience if the delict is intrinsically evil or tends to the harm of souls"
Read his Consecration Sermon and you can see that he acted out of grave fear. He believed that Pope John Paul had two years earlier broken the First Commandment by inviting false religions to pray to the devil in a Catholic Church for peace. He also believed that the prophecy of Our Lady at La Salette and Fatima was being fulfilled.
From his Sermon:
“….And I really believe that there has never been a greater iniquity in the Church than Assisi, which is contrary to the First Commandment of God and the First Article of the Creed. It is incredible that something like that could have ever taken place in the Church, in the eyes of the whole Church —how humiliating! We have never undergone such a humiliation! … And Our Lady prophesied for the 20th century, saying explicitly that during the 19th century and most of the 20th century, errors would become more and more widespread in Holy Church, placing the Church in a catastrophic situation. Morals would become corrupt and the Faith would disappear. It seems impossible not to see it happening today.
I excuse myself for continuing this account of the apparition, but she speaks of a prelate who will absolutely oppose this wave of apostasy and impiety —saving the priesthood by forming good priests. I do not say that prophecy refers to me. You may draw your own conclusions. I was stupefied when reading these lines but I cannot deny them, since they are recorded and deposited in the archives of this apparition.
Of course, you well know the apparitions of Our Lady at La Salette, where she says that Rome will lose the Faith, that there will be an “eclipse” at Rome; an eclipse, see what Our Lady means by this.
And finally, closer to us, the secret of Fatima. Without a doubt, the Third Secret of Fatima must have made an allusion to this darkness which has invaded Rome, this darkness which has invaded the world since the Council. And surely it is because of this, without a doubt, that John XXIII judged it better not to publish the Secret: it would have been necessary to take measures, such steps as he possibly felt himself incapable of doing, e.g., completely changing the orientations which he was beginning to take in view of the Council, and for the Council.”
sspx.org/SSPX_FAQs/appendix_v_1988_consecration_sermon.htm