7. 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.

19.

(. . .)

Let us pray that the errant be flooded with the light of his divine grace, may turn back from the path of error into the way of truth and justice and, experiencing the worthy fruit of repentance, may possess perpetual love and fear of his holy name.

6.

(. . .)

Do men like these pour forth their prayers to God that in His mercy he may bring to the Divine light of the Gospel by His victorious grace the people sitting in the darkness?

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?”

In an allocution to the cardinals on the Consistory of the 17th of December, 1847, Pius IX. congratulated the sacred college on the renewal of a cordial understanding with Spain, by means of which he had been enabled to appoint a number of bishops in that country once so devoted  to the Church. He alluded too to the favorable appearance of the Catholic cause in Russia, and repudiated certain theories ascribed to him. Against religious indifferentism so zealously advocated in our days, and made as it were a state creed, he said : "It is assuredly not unknown to you, venerable brethren, that in our times many of the enemies of the Catholic faith especially direct their efforts toward placing every monstrous opinion on the same level with the doctrine of Christ, or of confounding it therewith, and so they try more and more to propagate that impious system of the indifference of religions.

But quite recently, we shudder to say it, men have appeared who have thrown such reproaches upon our name and apostolic dignity, that they do not hesitate to slander us, as if we shared in their folly and favored the aforesaid most wicked system. From the measures, in no' wise incompatible with the sanctity of the  Catholic religion, which, in certain affairs relating to the civil government of the Pontifical States, we thought fit in kindness to adopt, as tending to the public advantage and prosperity, and from the amnesty graciously bestowed upon some of the subjects of the same States at the beginning of our pontificate, it appears that these men have desired to infer that we think so benevolently concerning every, class of mankind, as to suppose that not only the sons of the Church, but that the rest also, however alienated from Catholic unity they may remain, are alike in the way of salvation, and may arrive at everlasting life."

We are at a loss from horror to find words to express our detestation of this new and atrocious injustice that is done us. We do indeed love all mankind with the inmost affection of our heart, yet not otherwise than in the love of God, and of our Lord Jesus Christ, who came to  seek and to save that which had perished, who died for all, who wills all men to be saved, and to come to the knowledge of the truth ; who therefore sent his disciples into the whole world to preach the gospel to every creature, proclaiming that they who should believe and be baptized should be saved, but they who should believe not should be condemned ; who therefore will be saved let them come to the pillar and ground of faith, which is the Church; let them come to the true Church of Christ, which in its bishops and in the Roman Pontiff, the chief head of all, has the succession of apostolical authority, never at any time interrupted; which has never counted aught of greater moment than to preach and by all means to keep and defend the doctrine proclaim ed by the apostles, by Christ's command; which, from the apostles' time downward, has increased in the midst of difficulties of every kind ; and being illustrious through out the whole world by the splendor of miracles, multiplied by the blood of martyrs, exalted by the virtues of confessors and virgins, strengthened by the most wise testimonies of the fathers, hath flourished and doth flourish in all the regions of the earth, and shines refulgent in the perfect unity of the faith, of sacraments, and of holy discipline."

Allocution to the cardinals on the Consistory of the 17th of December, 1847, Pius IX:

It is assuredly not unknown to you, venerable brethren, that in our times many of the enemies of the Catholic faith especially direct their efforts toward placing every monstrous opinion on the same level with the doctrine of Christ, or of confounding it therewith, and so they try more and more to propagate that impious system of the indifference of religions.

But quite recently, we shudder to say it, men have appeared who have thrown such reproaches upon our name and apostolic dignity, that they do not hesitate to slander us, as if we shared in their folly and favored the aforesaid most wicked system.

(. . .) as to suppose that not only the sons of the Church, but that the rest also, however alienated from Catholic unity they may remain, are alike in the way of salvation, and may arrive at everlasting life."

We are at a loss from horror to find words to express our detestation of this new and atrocious injustice that is done us.

6There was a man sent from God, whose name was John.  7This man came for a witness, to give testimony of the light, that all men might believe through him.  8He was not the light, but was to give testimony of the light. 
9That was the true light, which enlighteneth every man that cometh into this world. 

Acts 8, 26:40

The issue I have trouble with regarding no salvation via invincible ignorance, is it means that there are entire continents where every single person for a thousand years was damned. Opponents of invincible ignorance say that in the case of a virtuous pagan following natural law, God would send a missionary over to them. So why is it that Europeans are so special and always had the faith, but there were entire continents of people where not a single soul was virtuous enough for salvation?  

The issue I have trouble with regarding no salvation via invincible ignorance, is it means that there are entire continents where every single person for a thousand years was damned. Opponents of invincible ignorance say that in the case of a virtuous pagan following natural law, God would send a missionary over to them. So why is it that Europeans are so special and always had the faith, but there were entire continents of people where not a single soul was virtuous enough for salvation?  

There's no evidence the Apostles ever reached America or Lapland, for example, so there's still a long time between the New Covenant and the arrival of Christian missionaries to those places. Even if we're to accept that they miraculously preached to those peoples and left no trace, why would everyone thereafter be punished for their fathers' sins?
I'm not some BODer at all, I give (I believe the term is) faithful assent to the fact that not even the so-called "invincibly ignorant" can be saved. But it's still an issue I have trouble with understanding.