Your understanding of Augustine is faulty.
"[N]othing could have been devised more likely to instruct and benefit the pious reader of sacred Scripture than that, besides describing praiseworthy characters as examples, and blameworthy characters as warnings, it should also narrate cases where good men have gone back and fallen into evil, whether they are restored to the right path or continue irreclaimable; and also where bad men have changed, and have attained to goodness, whether they persevere in it or relapse into evil; in order that the righteous may be not lifted up in the pride of security, nor the wicked hardened in despair of cure" (Against Faustus 22:96 [A.D. 400]).Augustine AGAINST Calvinist's false belief that one cannot lose one's salvation: it should also narrate cases where good men have gone back and fallen into evil, whether they are restored to the right path or continue irreclaimable
As the mystical body of Christ is the only one that wholly consists of believers, that is the one true church, while competition remains for those who will claim to be the one true visible church.
Like faith without works, the universal church, into which a believer is added at the moment of conversion, (1Coir. 12:13) even if in the desert (Acts 8:36-38) or before baptism (Acts 10:43-47; 15:7-9) always has a visible expression. And it is the Biblical gospel of grace - which can result in immediate conversion by convicted sinners, destitute of moral fitness and damned due to the lack of it, placing faith in the mercy of the Biblical God in the Biblical Christ for salvation on His blood expense and righteousness - that is the core truth of the church. This does relate to more than just the facts of the the gospel, as conviction of sin, righteousness and judgment presumes at least light of conscience, and trusting Christ to save infers Deity, yet as the Bible shows, the truth that results in the body of Christ having its members can be apprehended by a prepared soul quite readily.
And as by faith in the gospel of basic truths is how the church gains its members, then it militates against one particular group claiming to be the only true visible church. It is those who distort that and require membership in their particular church for salvation, as they are exclusive possessors of salvific truth, and requiring implicit trust in men, who are marked as “cults.”
An Eastern Orthodox bishop has expressed this doctrine as follows:[2]
“Extra Ecclesiam nulla salus. All the categorical strength and point of this aphorism lies in its tautology. Outside the Church there is no salvation, because salvation is the Church” (G. Florovsky, “Sobornost: the Catholicity of the Church”, in The Church of God, p. 53).
Does it therefore follow that anyone who is not visibly within the Church is necessarily damned? Of course not; still less does it follow that everyone who is visibly within the Church is necessarily saved.
As Augustine wisely remarked: “How many sheep there are without, how many wolves within!” (Homilies on John, 45, 12) While there is no division between a “visible” and an “invisible Church”, yet there may be members of the Church who are not visibly such, but whose membership is known to God alone. If anyone is saved, he must in some sense be a member of the Church; in what sense, we cannot always say. —Kallistos Ware
Protestants cannot say no one is saved in the RCC, nor can it claim it alone is the body of Christ, and it does nor, but the contention is when either is inferred, and which best represents the Bilical church, and upon what basis is that determined.
Calvin completely took Augustinian writings out of context and built a theology of double predestination out of sand. Whose understanding is faulty?