The puzzlement here, at least between the Orthodox and the Augustinians, was about the nature of Original Sin and the effects of that nature. To understand those, and in particular, to avoid a caricature of Catholicism that we saw on occasion on this thread, one must study the post-Augustinian teaching.
"Aren't the newborn (along with righteous pagans, etc.) destined to heaven through the operation of invincible ignorance?"
Perhaps you misspoke, which seems the simplest explanation for your later posts which don't seem to share this quite mistaken thought.
We must be careful not to veer into thinking as if Christ Himself is bound by His Sacraments.
Yet we also must be careful not to veer into thinking that He will not keep His promises. "Amen, amen, I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God." "Amen, amen, I say unto you: except you eat the flesh of the Son of man and drink his blood, you shall not have life in you."
One must be careful not to confuse what is frequently called Augustinism, especially by the Jansenists, Calvinists, and Lutherans, and what Catholics have taken from St. Augustine and incorporated as an explanation of the Faith.
Every system of grace expounded in Catholic theology, Augustinism, Thomism, Molinism, Congruism, Syncretism (all approved), Jansenism (condemned) claims to be teaching the exact truths St. Augustine attempted to communicate. Obviously St. Augustine did not teach all (or perhaps even any) of them, nor can they all be correct.
In any case, Catholics are not "Augustinians".