FSSP and SSPX priests need to know that there is a mistake in the Letter of the Holy Office and Vatican Council II.
Both documents mention hypothetical cases and assume they are explicit.Then they conclude that these explicit cases are objective exceptions to the Feeneyite interpretation of extra ecclesiam nulla salus (EENS).
In the Letter of the Holy Office 1949 the text in red type refer to hypothetical cases.However the Letter assumes they are explicit, objectively seen. This is the false premise.
Therefore, no one will be saved who, knowing the Church to have been divinely established by Christ, nevertheless refuses to submit to the Church or withholds obedience from the Roman Pontiff, the Vicar of Christ on earth.-Letter of the Holy Office 1949
In His infinite mercy God has willed that the effects, necessary for one to be saved, of those helps to salvation which are directed toward man's final end, not by intrinsic necessity, but only by divine institution, can also be obtained in certain circumstances when those helps are used only in desire and longing - Letter of the Holy Office 1949
but when a person is involved in invincible ignorance God accepts also an implicit desire,
Then follows the irrational conclusion of the Letter.The dogma EENS is contradicted.
Therefore, that one may obtain eternal salvation, it is not always required that he be incorporated into the Church actually as a member, but it is necessary that at least he be united to her by desire and longing.-Letter of the Holy Office 1949
The FSSP/SSPX priests use the same irrational premise to reach the same irrational conclusion.This was the initial mistake of Archbishop Lefebvre.
The same error is there in Lumen Gentium 14, Vatican Council II.
In the following passage from LG 14 the hypothetical passage (red) is placed along with the orthodox passage( blue) as if it is relevant or an exception.
14. This Sacred Council wishes to turn its attention firstly to the Catholic faithful. Basing itself upon Sacred Scripture and Tradition, it teaches that the Church, now sojourning on earth as an exile, is necessary for salvation. Christ, present to us in His Body, which is the Church, is the one Mediator and the unique way of salvation. In explicit terms He Himself affirmed the necessity of faith and baptism(124) and thereby affirmed also the necessity of the Church, for through baptism as through a door men enter the Church. Whosoever, therefore, knowing that the Catholic Church was made necessary by Christ, would refuse to enter or to remain in it, could not be saved.
They are fully incorporated in the society of the Church who, possessing the Spirit of Christ accept her entire system and all the means of salvation given to her, and are united with her as part of her visible bodily structure and through her with Christ, who rules her through the Supreme Pontiff and the bishops. The bonds which bind men to the Church in a visible way are profession of faith, the sacraments, and ecclesiastical government and communion. He is not saved, however, who, though part of the body of the Church, does not persevere in charity. He remains indeed in the bosom of the Church, but, as it were, only in a "bodily" manner and not "in his heart."(12*) All the Church's children should remember that their exalted status is to be attributed not to their own merits but to the special grace of Christ. If they fail moreover to respond to that grace in thought, word and deed, not only shall they not be saved but they will be the more severely judged.(13*)
Catechumens who, moved by the Holy Spirit, seek with explicit intention to be incorporated into the Church are by that very intention joined with her. With love and solicitude Mother Church already embraces them as her own.-Lumen Gentium 14
So you can affirm EENS and the passages in red would not be exceptions.
The FSSP/SSPX priests cannot affirm EENS ( Feeneyite) since the passages in red are explicit for them and so are exceptions to EENS and the passages in blue.
My Approach : apologetics
False reasoning from the Letter is all over Vatican Council II: Abp Lefebvre did not notice it -3