Presbyterians correctly claim that all such attempted 're-baptisms' are: unnecessary; impossible; and sinful. Exodus 4:24-26; Acts 8:12-24; Romans 4:11 & 6:1-5; First Corinthians 1:11-17 & 12:13; Ephesians 1:13f & 4:30f & 5:25f ; Colossians 2:11-13 & 3:10f ; Hebrews 6:1-6 & 10:22-39.
Indeed, even when administered irregularly (or when administered regularly) — Christian baptism, is Christian baptism. For there is only "one God and Father"; only "one body and one Spirit"; and only "one Lord, one faith, one baptism." Ephesians 4:4-6.
The "one baptism" of the Bible — is the baptism of the Lord Jesus as the only true Christ. It is baptism administered upon the authority, alias in the Name, of the one triune Jehovah Elohim. It is baptism administered into the Name of God; into the Father, Son and Holy Spirit; into the Ontological Trinity. Matthew 28:19; Mark 1:9-11 & 16:16; Genesis 1:1-3; Psalm 33:6; Romans 11:33-36; Second Corinthians 13:14; Revelation 4:3 to 5:7 & 22:16-18f.
The Triune God alone validates all things, including baptism. In all matters whatsoever — there can be no stronger or more valid point of reference, than He Himself.
Different deviations from primordial Presbyterianism
Triune baptisms alone are valid — wheresoever or by whomsoever administered. They are all obviously valid, whenever administered in the Church Universal of all the ages — re-formed and re-presbyterianized at the time of the Protestant Reformation. But they are also valid if performed in the post-patristic and deformed Roman Catholic Church — even today. Indeed, they are also valid, even if given by sectarian groups like the modern Seventh-day Adventists.
For reliance solely upon the saving Name of the Triune Elohim always been the position of God's Bible-believing Presbyterian Church worldwide. This has been the case, right down throughout all the centuries. Indeed, it is to be reliance on the Triune God alone — regardless of the place or the denomination where baptism into His Name was administered.
Such reliance has sufficed ever since the first presbyter (Adam), his wife (Eve), and their children (Abel and Seth) — even without baptism — trusted in Jehovah-Jesus for their salvation. Genesis 3:14-21; 4:1-4,26; 5:1-5f,23,29f; Hebrews 11:4-7; 12:22-24; First Peter 3:20f; Matthew 28:19.
True Presbyterians rely once and for all upon the Triune God alone. Thus they also insist on only "one baptism" — once and for all. For that is to point solely to Him. Ephesians 4:4-6.
Over against Presbyterianism, however, stand various varieties of Catabaptists. Such Catabaptists may be Romish, Baptistic, Quasi-Protestant, or Eastern Orthodox. In spite of all their differences with one another, they are all dissatisfied with a previous alleged baptism. Instead, they focus on the importance of undergoing a subsequent baptism — which alone they deem to be valid.
Catabaptists tend to rely more on the latter baptism itself than upon the Triune God to validate that sacrament. Holy Scripture, however, is quite plain. All 'rebaptisms' involve, at least subjectively, a fresh crucifying of Christ. Hebrews 6:1-6. The very idea should make Christians shudder. For Christ died but once and for all. In baptism, we too died once and for all. Romans 6:1-13.
Now Romish Catabaptists opt for an ex opere operato view of the sacrament. Thereby, baptism itself is deemed to cleanse. Although in theory they claim that 'Protestant baptisms' are quite valid -the Romanists' very insistence upon baptism as such, has expanded their giving 'conditional baptisms' to many and perhaps even to most Ex-Protestants who romanize. This itself makes such Romanist 'conditional baptizers' de facto Catabaptists.