If I had to describe the question that comes up most frequently in my various mailboxes by inquirers, it would be the following: how do you explain the historic position of the Catholic Church on extra ecclesiam nulla salus (outside the church there is no salvation), eens for short, ever since the 2nd Vatican Council changed this?
There are many ways to go about answering this question and if the inquirer is hungry enough, he won’t be satisfied until he has read at least a book or two on the matter. Since I don’t have the time and space to cook something for that purpose, I’d just like to make two points that many people who ask this question, given my personal experience, might not be aware of.
First, there exist authoritative sources from nearly 100 years before the convocation of the 2nd Vatican Council (4-5 generations of the pre-Vatican 2 episcopal college) that speak about the exceptional possibility of salvation for people who are neither united to the visible Catholic Church on earth (assembled under the Pope) nor even explicitly Christian by the confession of faith in Jesus Christ. Already in the 1860s, Pope Pius IX talks about this. More interestingly, the 1st draft for the constitution of the church that was due to be voted upon at the 1st Vatican Council (1870), c.f. Collectio Lacensis, VII, 567 ff., but which the Council never got to because of the abrupt halt to the Council due to the Franco-Prussian war, includes a rather robust statement on this matter (see linked article for citations).
Secondly, there is a way to speak about exceptions to the obvious necessity of being united visibly to the Catholic Church via baptism and profession of faith that does not effectively undo the original law of membership that came forth from the lips of Christ, i.e. “Whoever believes and is baptized will be saved” (Mk 16:16). Today, you might hear it said by some folks that the dogma of extra ecclesiam nulla salus is perfectly held intact when non-Catholics and non-Christians are treated as if they are fine as they are because, unbeknownst to them, they achieve unity with the Catholic Church through invisible means. Oh, I hardly see people (though I have and do) explicitly presuming this, but they can practically treat the matter this way.
In fact, this seems to have become the new norm. When was the last time you ever spoke with a person who told you their experience talking with their local Catholic priesthood about their joining the Catholic Church? 90% of the time they tell you that they were treated as if they were doing something ultimately unnecessary. In fact, we don’t even need to have this kind of firsthand account. It is the standard treatment between the chief Catholic hierarchy and the non-Catholic world that is recorded in countless video records only a google search away. Case in point, see the interaction between Pope Francis and Lutherans at the Vatican in the video linked in the comments. I need not remind those who were keeping tabs on the doings and goings about of Francis back when the Evangelical-Anglican bishop Tony Palmer, a personal friend of the Pope’s, was sharing his sincere interpretation of how the Jorge Bergoglio (they were friends far before his election to the supreme Pontificate) thought about the Protestant communities in ecumenical dialogue (also linked in the comments).
Now, persons such as Tony Palmer, Pope Francis, the Lutheran committees, and others who form these gatherings where everyone is at ease and feels equally accepted without any pressure to change one’s views, not least for the survival of their soul, are not unaware of the almost hidden, though explicit, statements in conciliar texts (Lumen Gentium 14-16) that state that Jesus Christ demands all men to formally join the Catholic Church, now assembled under the Cathedra of Unity occupied by Francis himself. They’ve done their homework, and those paragraphs don’t come as any surprise. Perhaps they see it as a happy inconsistency (I have no doubt some of them do), but they know enough to know it is there at a certain magnification of a microscope.
And yet, with this knowledge, they manage to act and dwell with one another as if there is no pressing need to change from any side, while also knowing the technicalities of Catholic doctrine. It is quite remarkable. Since when have Catholics, Orthodox, and Anglicans ever got together on the Vatican-level and ever felt the atmosphere get dense from a reminder that one among them is true and a binding necessity exists upon the conscience of all to fulfill the law of membership? Heck, one need only read Pope Francis’s recent “Diverse yet United: Communicating Truth in Charity”, which also has a foreword from Justin Welby, Archbishop of the Church of England, to see what kind of unity is prioritized by the Vatican these days. And lest my Orthodox readers think they have here an opportunity to get entertained by another Ybarra-editorial conceding problems within the RC, this same thing has been characteristic for more decades within Orthodoxy.
For decades now, we have even seen attempts to show that events such as the Assisi Prayer meetings (1896 & forward) or the joint-prayer meetings with Jews and Muslims, not to mention the recent “Smudging” ceremony hosted by Canadian officials in a meeting with the Pope (as participant), were all legitimate activities. And this despite the undeniable fact that the need to repetitively construct abstract and elaborated explanations over and over again to defend them as legitimate often contain enough proof in itself that there is a practical failure to shine forth the truth of the Church’s age-old law of membership, claimed to have been delivered by Christ Himself. At the end of the day, the nuanced distinctions that esoterically defend these actions are akin to having to magnify the scope 500x before you can even hope to see the faint existences of the dots and crosses that complete all the i’s and t’s.
This is also why proponents that defend these activities as legitimate, however much conceding imprudence, often see their skeptical interlocutors as unintelligent. They are so caught up and occupied with being 1000 feet deep in the weeds of all the “theology” that defends this kind of thing that they quite naturally look upon those not willing to embark upon such risky adventures as people who simply can’t intellectualize as well as they can.
Returning to the 2nd point, the mid-19th century all the way up to the Feeney controversy (1940s) showed how the Catholic Church did at one time express herself open to the availability, via extraordinary means, for extra ecclesia nulla salus to include non-Catholics, and even non-Christians (!), while also not falling into the practical eclipsing of the EENS law that I’ve described above in current times.
Lastly, I’m not here trying to pull everyone back to old times. I simply wanted to highlight 2 points that often get overlooked when people are pointing to the 2nd Vatican Council as the place where everything tanked on this question of eens.
https://erickybarra.wordpress.com/2019/08/11/vatican-iis-extra-ecclesiam-nulla-salus-precedents/?fbclid=IwAR3e8_siZh11WOeqQzKYAtdzQScDfPzcTrArr1H4C3d8GA76oNGjJXalXcg
Erick Ybarra 
Superbly done, Erick.
On my own blog I wrote this (altered here slightly to shorten it and make context clear):
The doctrine of extra ecclesiam nulla sullus has a lot of tension in it that can’t be merely resolved by throwing out Vatican II and Lumen Gentium, and it’s something that the Church has historically recognized. Note I say that it has *tension*. I do not think the doctrine is contradictory.
We can state it something like this:
Premise: Outside of the Catholic Church in union with the Pope of Rome there is no salvation
Premise: God desires all men to be saved
Premise: There are men alive who simply do not have the opportunity to join unity with the Pope of Rome
Conclusion: Either God does not desire all men to be saved (Which would disprove Catholicism anyway) or there is in fact salvation outside of the Catholic Church (which would disprove Catholicism’s claim to unique authority at the very least).
This is a serious and legitimate theological problem that Lumen Gentium and Vatican II actually try to *address* with their nuance. I am going off of memory here – this is not meant to be an exhaustive and academic case – but I believe Thomas Aquinas attempted to resolve the tension by positing that those with no opportunity to formally join the Catholic Church would be given the opportunity at the moment of their death. This is a perfectly logical proposition, but never formally defined, and the fact remains that in order for all of the things the Church claims about herself to be true the tension HAS to be addressed somehow.
Vatican II addressed the tension by formally defining a distinction between explicit and implicit unity and positing that men of good will who would reasonably desire to be a part of the Catholic Church if they were convinced of its truth could be said to be members implicitly, which is enough for salvation so long as one is not otherwise in a state of mortal sin.
This is as perfectly logical of a solution as Aquinas’s and, speaking personally for myself, has always satisfied me, but care must be taken not to lose sight of the enormous gap between a theoretical possibility that one MIGHT implicitly be a member of the Catholic Church and some sort of promise that everyone who means well is saved. That is not and cannot be what the teaching means.
These acts of Francis and those in the Vatican since the ‘Second Vatican Council’ show quite clearly that they do not profess the Catholic faith. It is true that they reduce the dogma ‘Extra Ecclesiam nulla salus’ to meaninglessness.
Also, none of Pope Pius IX’s teachings entail that non-Catholics can be saved. He denies this in a number of places, explicitly so in his profession of faith at the Vatican Council (1870).
+Fr. Michael Müller fantastically expounds the Catholic doctrine of salvation and invincible ignorance, which was Pope Pius IX’s view, in his book ‘The Catholic Dogma’:
http://traditionalcatholic.net/Tradition/Information/The_Catholic_Dogma/Chapter-V_Part-II.html#PART%20II