Concerning augustine and the fate of the unbaptized:
See
newadvent.org/fathers/15011.htm
On Merit and the Forgiveness of Sins, and the Baptism of Infants (Book I)
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Chapter 21 [XVI.]— Unbaptized Infants Damned, But Most Lightly; The Penalty of Adam’s Sin, the Grace of His Body Lost.**
It may therefore be correctly affirmed, that such infants as quit the body without being baptized will be involved in the mildest condemnation of all. That person, therefore, greatly deceives both himself and others, who teaches that they will not be involved in condemnation; whereas the apostle says: “Judgment from one offense to condemnation,” Romans 5:16 and again a little after: “By the offense of one upon all persons to condemnation.” Romans 5:18 When, indeed, Adam sinned by not obeying God, then his body— although it was a natural and mortal body— lost the grace whereby it used in every part of it to be obedient to the soul. Then there arose in men affections common to the brutes which are productive of shame, and which made man ashamed of his own nakedness. Genesis 3:10 Then also, by a certain disease which was conceived in men from a suddenly injected and pestilential corruption, it was brought about that they lost that stability of life in which they were created, and, by reason of the mutations which they experienced in the stages of life, issued at last in death. However many were the years they lived in their subsequent life, yet they began to die on the day when they received the law of death, because they kept verging towards old age. For that possesses not even a moment’s stability, but glides away without intermission, which by constant change perceptibly advances to an end which does not produce perfection, but utter exhaustion. Thus, then, was fulfilled what God had spoken: “In the day that you eat thereof, you shall surely die.” Genesis 2:17 As a consequence, then, of this disobedience of the flesh and this law of sin and death, whoever is born of the flesh has need of spiritual regeneration— not only that he may reach the kingdom of God, but also that he may be freed from the damnation of sin.
