SSPX can affirm Vatican Council II in harmony with EENS and appeal to all Catholics to do the same.

Here are citations from the Wikipedia entry on extra ecclesiam nulla salus(EENS) in which the popes affirm outside the Church there is no salvation without BOD,BOB and I.I referring to objective and known exceptions to EENS.

• Pope Pius IX The Syllabus of Errors, attached to Encyclical Quanta cura, 1864: [The following are prescribed errors:] ". Men can, in the cult of any religion, find the way of eternal salvation and attain eternal salvation. - Encyclical Qui pluribus, November 9, 1846. ". One ought to at least have good hope for the eternal salvation of all those who in no way dwell in the true Church of Christ. - Encyclical Quanto conficiamur moerore, August 10, 1863, etc."
• Pope Leo XIII (1878–1903), Encyclical Annum ingressi sumus: "This is our last lesson to you; receive it, engrave it in your minds, all of you: by God's commandment salvation is to be found nowhere but in the Church." idem, Encyclical Sapientiae christianae: "He scatters and gathers not who gathers not with the Church and with Jesus Christ, and all who fight not jointly with Him and with the Church are in very truth contending against God."
• Pope St. Pius X (1903–1914), Encyclical Jucunda sane: "It is our duty to recall to everyone great and small, as the Holy Pontiff Gregory did in ages past, the absolute necessity which is ours, to have recourse to this Church to effect our eternal salvation."
• Pope Benedict XV (1914–1922), Encyclical Ad Beatissimi Apostolorum: "Such is the nature of the Catholic faith that it does not admit of more or less, but must be held as a whole, or as a whole rejected: This is the Catholic faith, which unless a man believe faithfully and firmly, he cannot be saved."
• Pope Pius XI (1922–1939), Encyclical Mortalium Animos: "The Catholic Church alone is keeping the true worship. This is the font of truth, this is the house of faith, this is the temple of God; if any man enter not here, or if any man go forth from it, he is a stranger to the hope of life and salvation… Furthermore, in this one Church of Christ, no man can be or remain who does not accept, recognize and obey the authority and supremacy of Peter and his legitimate successors."
• Pope Pius XII (1939–1958), Encyclical Humani Generis, August 12, 1950: "Some reduce to a meaningless formula the necessity of belonging to the true Church in order to gain eternal salvation."
• Pope Pius XII (1939–1958), Allocution to the Gregorian University (17 October 1953): "By divine mandate the interpreter and guardian of the Scriptures, and the depository of Sacred Tradition living within her, the Church alone is the entrance to salvation: She alone, by herself, and under the protection and guidance of the Holy Spirit, is the source of truth."
• https://en.wikipedia.org/wiki/Extra_Ecclesiam_nulla_salus

These are traditional citations on EENS from Wikipedia's entry on extra ecclesiam nulla salus. So until 1958 the popes were affirming EENS without BOD, BOB and I.I referring to objective and known cases.

Wikipedia's next entry is from Vatican Council II, influenced by the Letter of the Holy Office and so the change in theology and doctrine was made.

Here Pope Pius IX affirms traditional EENS without the BOD, BOB and  I.I confusion. He is in line with Fr. Leonard Feeney and the missionaries in the 16th century.
So in  1878 things were still looking good.

Pope Pius IX (1846–1878), Encyclical Singulari quidem March 17, 1856): "Teach that just as there is only one God, one Christ, one Holy Spirit, so there is also only one truth which is divinely revealed. There is only one divine faith which is the beginning of salvation for mankind and the basis of all justification, the faith by which the just person lives and without which it is impossible to please God and come to the community of His children (Romans 1; Hebrews 11; Council of Trent, Session 6, Chapter 8). There is only one true, holy, Catholic Church, which is the Apostolic Roman Church. There is only one See founded on Peter by the word of the Lord (St. Cyprian, Epistle 43), outside of which we cannot find either true faith or eternal salvation. He who does not have the Church for a mother cannot have God for a father, and whoever abandons the See of Peter on which the Church is established trusts falsely that he is in the Church (ibid, On the Unity of the Catholic Church). ... Outside of the Church, nobody can hope for life or salvation unless he is excused through ignorance beyond his control."

• https://en.wikipedia.org/wiki/Extra_Ecclesiam_nulla_salus

"Here, too, our beloved sons and venerable brothers, it is again necessary to mention and censure a very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion. Sincerely observing the natural law and its precepts inscribed by God on all hearts and ready to obey God, they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace. Because God knows, searches and clearly understands the minds, hearts, thoughts, and nature of all, his supreme kindness and clemency do not permit anyone at all who is not guilty of deliberate sin to suffer eternal punishments."

"Also well known is the Catholic teaching that no one can be saved outside the Catholic Church. Eternal salvation cannot be obtained by those who oppose the authority and statements of the same Church and are stubbornly separated from the unity of the Church and also from the successor of Peter, the Roman Pontiff, to whom 'the custody of the vineyard has been committed by the Savior.' The words of Christ are clear enough: 'If he refuses to listen even to the Church, let him be to you a Gentile and a tax collector;' 'He who hears you hears me, and he who rejects you, rejects me, and he who rejects me, rejects him who sent me;' 'He who does not believe will be condemned;' 'He who does not believe is already condemned;' 'He who is not with me is against me, and he who does not gather with me scatters.' The Apostle Paul says that such persons are 'perverted and self-condemned;' the Prince of the Apostles calls them 'false teachers . . . who will secretly bring in destructive heresies, even denying the Master. . . bringing upon themselves swift destruction.'"

(Pope Pius IX, Quanto Conficiamur Moeroore, 7-8)

Pope BI. Pius IX - August 10, 1863)

Lionel:

Pope Pius IX in 1863 is affirming the traditional interpretation of the dogma EENS in the passages marked in blue.The liberal theologians have re-interpreted the passages in red as referring to visible and known people saved outside the Church, without the baptism of water.

The passages in red are, for me, hypothetical cases, possibilities known only to God and if they existed it would include the baptism of water in the Catholic Church since this is the dogmatic teaching.

However the important point is, that with or without the baptism of water, they are invisible cases for us human beings.So they never ever were exceptions to EENS.

After 1958 the mistake was accepted in the Church. The mistake is there in Vatican Council II too.

Now the SSPX has to realize that BOD, BOB and I.I are not visible cases. So they are not exceptions to Feeneyite EENS. The SSPX must accept Feeneyite EENS. This is the first step towards their reconcilation.

Then they have to realize that like BOD, BOB and I.I, LG 16, LG 8, LG 14, UR 3, NA 2, GS 22, AG 11, AG 7 etc also refer to hypothetical cases. They are not references to known people saved outside the Church.So Vatican Council II is not a rupture with the Feeneyite interpretation of the dogma EENS. The SSPX can affirm Vatican Council II in harmony with EENS and appeal to all Catholics to do the same.

So since they would be accepting Vatican Council II they can ask to be given canonical status. -Lionel Andrades

http://www.sanpiox.it/