CathInfo.com

https://www.cathinfo.com/baptism-of-desire-and-feeneyism/why-do-all-major-trad-organisations-teach-those-in-false-religions-can-be-saved/msg661645/#msg661645

Are you sure you've not mis-assessed the position of those you mention in your OP?  The claim that ABL and the CMRI are each committed to Vatican II soteriology is one that crops up again and again, but I've never seen sufficient evidence that this is the case for either.

Unitatis Redintegratio, Decree on Ecuмenism

http://www.vatican.va/archive/hist_councils/ii_vatican_council/docuмents/vat-ii_decree_19641121_unitatis-redintegratio_en.html

3.

(. . .)

Moreover, some and even very many of the significant elements and endowments which together go to build up and give life to the Church itself, can exist outside the visible boundaries of the Catholic Church: the written word of God; the life of grace; faith, hope and charity, with the other interior gifts of the Holy Spirit, and visible elements too. All of these, which come from Christ and lead back to Christ, belong by right to the one Church of Christ.

Dominus Iesus

http://www.vatican.va/roman_curia/congregations/cfaith/docuмents/rc_con_cfaith_doc_20000806_dominus-iesus_en.html

12.

(. . .)

Furthermore, the salvific action of Jesus Christ, with and through his Spirit, extends beyond the visible boundaries of the Church to all humanity. Speaking of the paschal mystery, in which Christ even now associates the believer to himself in a living manner in the Spirit and gives him the hope of resurrection, the Council states: “All this holds true not only for Christians but also for all men of good will in whose hearts grace is active invisibly. For since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partners, in a way known to God, in the paschal mystery”.37

(37) Second Vatican Council, Pastoral Constitution Gaudium et spes, 22.

CCC, 847:

https://www.catholicculture.org/culture/library/catechism/index.cfm?recnum=3077

Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.

Lumen Gentium, Dogmatic Constitution on the Church

http://www.vatican.va/archive/hist_councils/ii_vatican_council/docuмents/vat-ii_const_19641121_lumen-gentium_en.html

15. The Church recognizes that in many ways she is linked with those who, being baptized, are honored with the name of Christian, though they do not profess the faith in its entirety or do not preserve unity of communion with the successor of Peter.

( . . .)

They also share with us in prayer and other spiritual benefits. Likewise we can say that in some real way they are joined with us in the Holy Spirit, for to them too He gives His gifts and graces whereby He is operative among them with His sanctifying power.

16.

(. . .)

Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience.(19*) Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life.

CCC 1281

http://www.vatican.va/archive/ccc_css/archive/catechism/p2s2c1a1.htm\

Those who die for the faith, those who are catechumens, and all those who, without knowing of the Church but acting under the inspiration of grace, seek God sincerely and strive to fulfill his will, can be saved even if they have not been baptized (cf. LG 16).

An Interview with Karl Rahner on the State of Catholic Theology Today

http://www.innerexplorations.com/chtheomortext/kr.htm

Toe: Tell us something about your ideas on what you call anonymous Christianity.



Rahner: "Anonymous Christianity means that a person lives in the grace of God and attains salvation outside of explicitly constituted Christianity… Let us say, a Buddhist monk… who, because he follows his conscience, attains salvation and lives in the grace of God; of him I must say that he is an anonymous Christian; if not, I would have to presuppose that there is a genuine path to salvation that really attains that goal, but that simply has nothing to do with Jesus Christ. But I cannot do that. And so, if I hold if everyone depends upon Jesus Christ for salvation, and if at the same time I hold that many live in the world who have not expressly recognized Jesus Christ, then there remains in my opinion nothing else but to take up this postulate of an anonymous Christianity."¹¹

http://www.dailycatholic.org/issue/08Aug/aug4str.htm


Against the Heresies, by Archbishop Marcel Lefebvre: Page 216:

Evidently, certain distinctions must be made. Souls can be saved in a religion other than the Catholic religion (Protestantism, Islam, Buddhism, etc.), but not by this religion. There may be souls who, not knowing Our Lord, have by the grace of the good Lord, good interior dispositions, who submit to God...But some of these persons make an act of love which implicitly is equivalent to baptism of desire. It is uniquely by this means that they are able to be saved.

Against the Heresies, by Archbishop Marcel Lefebvre: Page 217:

"One cannot say, then, that no one is saved in these religions…"

Against the Heresies, by Archbishop Marcel Lefebvre: Pages 217-218:

"This is then what Pius IX said and what he condemned. It is necessary to understand the formulation that was so often employed by the Fathers of the Church: 'Outside the Church there is no salvation.' When we say that, it is incorrectly believed that we think that all the Protestants, all the Moslems, all the Buddhists, all those who do not publicly belong to the Catholic Church go to hell. Now, I repeat, it is possible for someone to be saved in these religions, but they are saved by the Church, and so the formulation is true: Extra Ecclesiam Nulla Salus. This must be preached."

Bishop Lefebvre, Sermon at first Mass of a newly ordained priest (Geneva: 1976):

"We are Catholics; we affirm our faith in the divinity of Our Lord Jesus Christ; we affirm our faith in the divinity of the Holy Catholic Church; we think that Jesus Christ is the sole way, the sole truth, the sole life, and that one cannot be saved outside Our Lord Jesus Christ and consequently outside His Mystical Spouse, the Holy Catholic Church. No doubt, the graces of God are distributed outside the Catholic Church, but those who are saved, even outside the Catholic Church, are saved by the Catholic Church, by Our Lord Jesus Christ, even if they do not know it, even if they are unaware of it..."

Fr. Schmidberger (SSPX), Time Bombs of the Second Vatican Council, 2005, p. 10:

"Ladies and gentlemen, it is clear that the followers of other religions can be saved under certain conditions, that is to say, if they are in invincible error."

Bishop Bernard Fellay, Superior General of SSPX, Conference in Denver, Co., Feb. 18, 2006:

Consider a Hindu in Tibet who has no knowledge of the Catholic Church. He lives according to his conscience and to the laws which God has put into his heart. He can be in the state of grace, and if he dies in this state of grace, he will go to Heaven."

The SSPV, The Roman Catholic, Fenton Article, Fall 2003, p. 6:

"So, is it true and an article of faith that 'outside the Church there is no salvation'? Yes, it is. Does this mean that a person, no matter how praiseworthy a life he may have led, will be eternally lost who, through no grave fault of his own, is not an actual member of the Church at the moment of death? No, it does not."

The SSPV, The Roman Catholic, Fenton Article, Fall 2003, p. 7:

"With the strict, literal interpretation of this doctrine, however, I must take issue, for if I read and understand the strict interpreters correctly, nowhere is allowance made for invincible ignorance, conscience, or good faith on the part of those who are not actual or formal members of the Church at the moment of death. It is inconceivable to me that, of all the billions of non-Catholics who have died in the past nineteen and one-half centuries, none of them were in good faith in this matter and, if they were, I simply refuse to believe that hell is their eternal destiny."

Bishop Donald Sanborn, Sacerdotium V, p. 24:

"Vatican II's idea of the Church is heretical, since it identifies organized religions of pagans and idolaters with the Mystical Body of Christ. The truth is that in no way are pagans and idolaters, as pagans and idolaters, united to the Mystical Body of Christ. If, by some mystery of Providence and Predestination, they [pagans and idolaters] are united to the soul of the Church, and by desire to its body, it is in spite of their paganism and idolatry. It is due to an invincible ignorance of their error."

Fr. Kevin Vaillancourt, I Baptize With Water, p. 18, quoting from Fr. Tanquery with approval:

"Necessity of means, however, is not an absolute necessity, but a hypothetical one. In certain particular circuмstances, for example, in the case of the invincible ignorance or of incapability, actual membership in the Church can be supplied by the desire for this membership. It is not necessary that this be explicitly present; it can be included in a willingness and readiness to fulfill the will of God. In this way those who are outside the Catholic Church can achieve salvation." (Catholic Research Institute)

Fr. Kevin Vaillancourt, I Baptize With Water, p. 17:

"Are there any more 'good faith' pagans in existence? Is it possible for the Communists of China or the faithful adherents of Buddhism and Mohammedism of the Near and Far East to either have never heard the Gospel, or else had the Gospel presented to them in an erroneous light?... Can the Chinese Communist, or the Indian Buddhist or the Pakistani Muslim be included in such a consideration [of invincible ignorance]? Only God knows, and it is not up to me to decide for Him. I write here merely to uphold the dogmatic principle of the possibility of such cases today, without admitting that all, or even a significant number of those who are in such circuмstances will achieve salvation through justification."

Gregory XVI, Mirari Vos, 1832

http://www.papalencyclicals.net/greg16/g16mirar.htm

13. Now We consider another abundant source of the evils with which the Church is afflicted at present: indifferentism. This perverse opinion is spread on all sides by the fraud of the wicked who claim that it is possible to obtain the eternal salvation of the soul by the profession of any kind of religion, as long as morality is maintained. Surely, in so clear a matter, you will drive this deadly error far from the people committed to your care. With the admonition of the apostle that “there is one God, one faith, one baptism”[16] may those fear who contrive the notion that the safe harbor of salvation is open to persons of any religion whatever. They should consider the testimony of Christ Himself that “those who are not with Christ are against Him,”[17] and that they disperse unhappily who do not gather with Him. Therefore “without a doubt, they will perish forever, unless they hold the Catholic faith whole and inviolate.”[18] Let them hear Jerome who, while the Church was torn into three parts by schism, tells us that whenever someone tried to persuade him to join his group he always exclaimed: “He who is for the See of Peter is for me.”[19] A schismatic flatters himself falsely if he asserts that he, too, has been washed in the waters of regeneration. Indeed Augustine would reply to such a man: “The branch has the same form when it has been cut off from the vine; but of what profit for it is the form, if it does not live from the root?”