Basic false premises:
A.) The Church of Christ (COC) does not recognize how many types of baptism are in the Bible.
#1.) God pouring out the flood in judgment [a water pouring with the end result being immersion] according to 1 Peter 3:20-21. ("baptism doth ALSO NOW")
#2.) The identification of the Israelites with Moses, God's messenger. (1 Corinthians 10:1-2) There was no immersion, the baptism was completely dry.
#3.) Water baptism as a "like figure" of the washing away of sins (Acts 2:38, Acts 22:16, 1 Peter 3:21, Matthew 3, etc.)
#4.) Baptism with fire, another judgement baptism. This one being into hell fire (Matthew 3:10-12, 2 Thessalonians 1:7-10, Revelation 20:15).
#5.) Baptism of suffering/death (Matthew 20:22, Mark 10:38, Luke 12:50).
#6.) Baptism BY Christ WITH the Holy Ghost ONTO a person (Matthew 3:11, Acts 2:38, Ezekiel 36:27, Joel 2:28, Jeremiah 32:39, Acts 8:15-17, Acts 10:44-48, Acts 19:6, etc.)
#7.) Baptism BY the Spirit WITH a person INTO Christ, an "operation of God" (Colossians 2:10-12, 1 Corinthians 12:12-13, Galatians 3:26-28, Romans 6:3-4).
B.) The Church of Christ (COC) does not recognize Paul as the distinct "apostle to the Gentiles", "the pattern to them which should hereafter believe", and the one who Christ dispensed the revelation of the mystery and gospel of the grace of God to (Romans 11:13, Galatians 1:11-12, Galatians 2:7-8, 1 Corinthians 15:1-4, 2 Timothy 2:7, 2 Timothy 2:15, Ephesians 3:1-9, Romans 16:25-26, Colossians 1:25-27, Ephesians 5:22-32, 1 Timothy 1:12-16, Romans 11:25, 1 Corinthians 3:10, 1 Corinthians 4:16, 1 Corinthians 11:1-2, 1 Corinthians 4:1, etc.)
If the COC's would recognize those truths they would find their answers to buptismal regeneration. Let's examine their proof texts and refute the heresy of baptismal regeneration.
1.) Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. (ditto Mark 1:4, Luke 3:3)
In none of those passages (Acts 2:38, Mark 1:4, Luke 3:3) has the revelation of the mystery and gospel of the grace of God been dispensed yet. The body of Christ had not yet begun and Peter was looking FORWARD to the 2nd coming of Christ for remission of sins (Acts 3:19-26, 1 Peter 1:7-11) and the restoration of Israel (Acts 3:19-26, Acts 1:6). Peter knew nothing about preaching Jesus Christ according to the revelation of the mystery which had been kept secret since the world began nor the blindness of Israel until the fullness of the Gentiles be come in (Romans 11:13, 25, 16:25-26). Peter was preaching the Old Testament prophecy of the New Covenant which brought Israel remission of sins at the 2nd coming after the tribulation period (Jer. 31:31-34, 32:37-42, Ezek. 36:24-31, 1 Pet. 1:7-10, Acts 3:19-26).
So to apply Acts 2:38 to this age (Eph. 2:13) is out of the question. But even in this context of the gospel of the kingdom (Matt. 4:23, 9:35, 24:14, Mark 1:14), the water baptism would not regenerate the soul. That is the work of the Holy Spirit and the blood of Christ. Water baptism was only a "like figure" of the washing away of sins that did not put away the filth of the flesh (Acts 22:16, 1 Peter 1:18-25, 1 Peter 3:21).
Here are some irrefutable facts about Acts 2: Peter knew nothing about the dispensation of grace, The body of Christ, the pre-trib rapture of the body of Christ, complete salvation before the 2nd coming (he thought it came at the 2nd coming), Peter would not preach to Gentiles without Jews present until Israel repented (Luke 24:47), Peter did not preach that Christ died for sins in Acts 2 (he only preached a murder charge against the Jews), Peter and the apostles were still keeping the law (Acts 2:46, Acts 10:1-14, Acts 15), those in Acts 2 were keeping Christ's commandment to sell all that they had (Matthew 19:16-23, Matthew 10:9-10, Acts 2:44-45, Acts 4:34-37, 5:1-11).
Those are irrefutable facts about Acts 2.
Also, the plan of salvation was already given before verse 38....
Acts 2:21 And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved.
Then Peter proves that Christ rose from the dead and is God and King over Israel (v. 22-36). So before we even get to verse 38 the plan of salvation has been given. Now look at verses 37-38.
"Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do? Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost."
Clearly these Jews had already called on the name of the Lord and believed that Christ was God and King over Israel, or else they would not have felt "pricked in their heart". These Jews did not ask "what shall we do to be saved" because Peter already declared in verse 21 that "whosoever shall call on the name of the Lord shall be saved". What these Jews ARE ASKING is what should they do now....since they crucified their Messiah, which was Peter's charge against them (Acts 2:22-36).
The answer to that was the following:
1.) Repent of it
2.) Get water baptized to answer God with a good conscience (1 Peter 3:21)
"FOR the remission of sins" does not mean "to obtain the remission of sins". It means 'BECAUSE OF' the remission of sins......look at the references yourself.
 Lest any should say that I had baptized in mine own name.
 And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
 For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.
 And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree:
 Him God raised up the third day, and shewed him openly;
 Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead.
 And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead.
 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.
 For they heard them speak with tongues, and magnify God. Then answered Peter,
 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?
 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
 And all the people that heard him, and the publicans, justified God, being baptized with the baptism of John.
 But the Pharisees and lawyers rejected the counsel of God against themselves, being not baptized of him.
 For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
 And with many other words did he testify and exhort, saying, Save yourselves from this untoward generation.