It occurs to me based on the material I have examined, that Tascius Caecilius Cyprianus (aka Saint Cyprian), and the Orthodox who follow his view of rebaptizing heretics, are wrong.
Here are my reasons:
Pope Saint Stephen disagreed with Cyprian. Stephen had greater authority then Cyprian, being Pontiff of the Apostolic See in Rome.
Cyprian cited a fragment from Stephen's decree which said:
"If anyone comes to you from any heresy whatsoever, let there be no innovation, but observe what has been handed down..." [Corpus Scriptorum Christianorum Orientalium, Paris 1903-3:799-800,805].
The statement above shows Cyprian's view was an innovation and violated the teaching of the Church which was handed down.
Bishop Firmilian of Caesarea supported Cyprian on this. Regarding Pope Stephen Firmilian stated:
"....Stephen , who preaches that he has the chair of Peter by succession, is moved by no zeal against the heretics..." [Cyprian Ep. 75, CSEL 3:821].
A century and a half later, commenting on the controversy, St. Jerome wrote:
"Blessed Cyprian... condemning the baptism of heretics, sent [the acts of] an African Council on this matter to Stephen, who was then bishop of the city of Rome, and the twenty-second from Blessed Peter; but his attempt was in vain. Eventually the very same bishops, who had laid down with him that heretics were to be rebaptized, returning to the ancient custom, published a new decree [Contra Lucif., 23. PL 23:186].
We see in the above that Cyprian recognized the authority / opinion of Stephen by sending him the acts of an African Council.
We also see that the bishops who had originally agreed with Cyprian, "returned to the ancient custom." This shows the ancient custom was not in favor of Cyprian, according to Jerome.
Augustine later stated:
"I do not accept what Blessed Cyprian thought about baptizing heretics and schismatics, because the Church, for which Blessed Cyprian shed his blood, does not accept this" [Contra Cresc.II, 32].
We see in the above quote that the church did not accept Cyprian's view. The Pope and universal Church had more authority then Cyprian.
But Augustine insisted, Cyprian remained "in catholic unity," and whatever correction Cyprian needed was compensated by his abundant charity, and the purification of suffering. [De Bapt. I, 18. PL 43: 125-6, 465, 490].
The position of the "rebaptizers" was repudiated even by heretics. Patriarch Severus of Antioch, who was excommunicated by Pope St. Symmachus [498-514] did not agree with Cyprian. [Ed. E.W. Brooks. The Sixth Book of the Select Letters...2:314].
'LET THERE BE NO INNOVATION" (NIHIL INNOVETUR)
The words nihil innovetur --- let there be no innovation! remind us that Stephen had invoked his power not in favor of doctrinal novelty, but to preserve the ancient practice of the Church. Two centuries later, in a work known as the Commonitorium, Vincent of Lerins wrote:
"Agrippinus of venerable memory, who was once bishop of Carthage, first of all mortals, against the divine Canons, against the rule of the Universal Church, against the opinion of all his fellow priests, against the custom and institutions of the elders, thought that rebaptism ought to be practiced...Then Pope Stephen of blessed memory, bishop of the Apostolic See, together indeed with the rest of his colleagues but more than the others, resisted, thinking it fitting, I think, that that he exceed all the rest as much by the devotion of his faith as he did by the authority of his place. What happened in the end? What force was there in the African Council or decree? By God's gift, none. Everything, as if a dream or story, was trampled upon as useless, abolished, superseded..." [PL 50:645-6].
Saint Vincent of Lerins did not agree with Cyprian.
I wonder how Orthodox and "rebaptizers" deal with these facts.