For the God of the Old Testament, Jehovah ’Elohiym, is the Triune God of the New Testament -the Father and the Son and the Holy Spirit. Valid baptism is always into His Name alone. The Post-Christian Judaists, Muslims and Jehovah witnesses have rejected this Triune God — in favour of Unitarianism. They all need to be baptized. The Hindus and the Mormons have rejected this Triune God — in favour of Polytheism. They too all need to be baptized.
Agnostics have rejected God Triune — in favour of ignorance. Atheists have rejected God Triune -in favour of matter. Buddhists have rejected God Triune, in favour of knowledge. Humanists have rejected God Triune, in favour of humanity. All of them need to repent, and to be baptized.
But Baptists, Campbellites, Eastern-Orthodox, Lutherans, Methodists, Romanists and Seventh-day Adventists — in spite of their various soteriological errors — do not need to be (re)baptized. For all of them, already, have been baptized quite validly — as Trinitarians — in the Name of the Father and
of the Son and of the Holy Spirit. What they need to do, is to repent — to turn to the Triune God of their baptism with a better understanding, and with all their hearts.
Adamic Presbyterianism: mankind's first religion
The Presbyterian Church, as its very name would indicate, is quite the oldest denomination on earth. For it was established by the Triune God (Jehovah Elohim) in the Garden of Eden, with its covenant head Adam as its very first 'presbyter' (or mature Elder). Genesis 1:1-28f & 2:4-24 & 3:15f; First Timothy 2:12 to 3:5; Hebrews 11:1-4f.
The Christian Church is to be presbyterian. Exodus 3:6-18; 18:12-21; Matthew 16:18f ; 18:15-17; 22:31f ; Hebrews 11:2; 12:22-24; 13:7,17,34. Indeed, during the future triumph of Christianity here on earth — as a result of the vigorous preaching of the Word and the faithful 'presbyterian' administration of the sacraments, the government of the Church Visible Universal — will become more and more presbyterian. Thus compare: Isaiah 2:2-4f ; Zechariah 12:6f ; Revelation 4:4-11; 5:6-14; 11:15-17; Westminster Larger Catechism 191.
Now Presbyterians sprinkle their baptizees — upon the authority and into the Name of the Triune God. Psalms 72:6-11; 77:15-20; Isaiah 44:1-4; 52:15f ; Ezekiel 36:25; Acts 1:5f ; 2:3,17,33,38f ; First Corinthians 10:1-2; Hebrews 6:2-7; 9:10-21; 10:22.
See too Dr. Francis Nigel Lee's 1990 monograph Sprinkling is Scriptural. This Biblical baptism by sprinkling incorporates them into the Christian Church Visible as the earthly body of Christ — the religious community consisting of those already considered to be "Christians" (by grace and through faith only in the merits of Jesus Christ).
They are so deemed — because they are priorly considered to be "Christians and federally holy before baptism." Thus, the Westminster Assembly's Directory for the Publick Worship of God — in the section on the administration of the sacraments (and first, of baptism).
Presbyterians fully realize that many baptizees — especially those who later transfer their Christian membership from elsewhere to the Presbyterian Church — were, unfortunately, not Christians before and at the time of their baptisms. Of course, they certainly should have been. Yet sadly, many were not.
Most professing Christians and their children who transfer to the Presbyterian Church, were baptized previously — but some of them only by way of submersion. Though such immersion is irregular, it is nevertheless valid.
Hence, Presbyterians would never wish to 're-baptize' — not even by the right mode of sprinkling -those previously baptized simply by submersion. Westminster Confession of Faith 28:3. For