Could you try looking at the passage from Pius IX without assuming there's a contradiction? What does it say, then? And you shouldn't neglect the context - it is important to understanding what it says from the BOD perspective.
I am the one telling you that there is no contradiction. Before the text, he affirms EENS, after the text, he affirms EENS, the text itself *must* agree with what he said before and after it and also affirm EENS. This is elementary.
"When you do not understand what is written, you must read what is written directly before and after to read it in context to understand what it means". - Second grade teacher.
Here is a break down:
"There are, of course, those who are struggling with invincible ignorance about our most holy religion".Note that the person is not invincibly ignorant or some native on a desert island. Rather, the person is normal, has intellect, knows how to think and is intelligent in things other than our holy religion but who now struggles with his invincible ignorance about our holy religion, which means he is sincerely trying to find out about our 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". All human creatures have inscribed by God on their hearts how to live according to the natural law and it's precepts, and to obey God is part of the natural law.
As long as a person does both; 1) seeks to find out about our holy religion and 2) strives to live according to the natural law and it's precepts, God will lead that person into the Church just as He led you into the Church and will never abandon that person. This is simply the very same Divine Providence that God arranged for you and I and all who are members to be in the Church. It is by the very same Providence He can arrange for anyone else who desires or is willing to enter it.
Once inside the Church, like you and I, he also is able to attain eternal life - provided he, like you and I, cooperates with the efficacious virtue of divine light and grace. Note that living a virtuous life is not enough and is in fact worthless without also seeking to find our about our holy religion. The pope rightly decries the necessity of both.
"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".Such a person does not exist outside of the Church, as the pope immediately reiterates:
"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".Put it all together:
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".