The evidence for baptismal regeneration in the New Testament is simply overwhelming. For articles discussing this, see, for example:
Even for those who belong to traditions that reject baptismal regeneration, when they are intellectually honest, will admit that baptism positive affects salvation, and is not purely symbolic, in texts such as Rom 6:1-5. The NASB renders the text as follows:
What shall we say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it? Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. For if we have become united with Him in the likeness of His death, certainly we shall also be in the likeness of His resurrection.
Leon Morris, a Reformed Protestant scholar, wrote the following about Paul’s teachings on water baptism in Rom 6:3-5:
Paul turns to baptism, which is perhaps surprising . . . Baptism, so to speak, incorporates the baptized into Christ; they are baptized “into one body” (1 Cor. 12:13), made part of that body which is the body of Christ (cf. SH, “’were baptized into union with’ [not merely ‘obedience to’] ‘Christ’. The act of baptism was an act of incorporation into Christ”). This can be made a little more precise. Those so baptized were baptized into his death . . . It is the death of Christ that makes anyone a Christian, and apart from that death baptism is meaningless . . . Being united in living out the life is not an option but a necessary part of being saved in Christ . . . When we are baptized we have died. In baptism we are buried with Christ. An old way of life passes away completely.
But that is not the whole story; the death has its purpose; it is with a view to something further. The parallel with Christ is followed through. His death was followed by resurrection, and our death to sin and our baptism into his death are followed by our being raised to new life. Paul uses aorists in his verbs were buried and was raised. They give a note of decisiveness to the rising to new life. (Leon Morris, The Epistle to the Romans [Grand Rapids, Mich.: Eerdmans, 2012], 246, 247, 248-49)
Tony Costa, another Reformed Protestant, discusses the salvific nature of water baptism in Paul's theology in Rom 6 thusly in a section entitled, "Baptism as Identification":
The first thing we note is that Paul equates being baptized into Christ as being baptized into his death (Rom 6:3). Here Paul employs a metaphor. The believer does not necessarily die in baptism in a physical sense, but he or she is described as dying with Christ by way of spiritual analogy. They have died to their old self (cf. 2 Cor 5:17). Here we see baptism functioning as an identity marker in that the believer in baptism is identified with Christ in his death. Another metaphor that Paul includes with baptism is that of the believer in baptism being identified with Christ in his burial (Rom 6:4), but again this is not literal but metaphorical. Paul proceeds to use a third metaphor in relation to baptism to show that as Christ was raised from the dead to a new life by the glory of the Father, so believers have been identified with him to walk in a new life on a spiritual plane (Rom 6:4). This new life vis-á-vis baptism is often marked by calls and exhortations to ethical living . . . Paul reasons that since Christian believers are united by baptism with Jesus in his death, they will also consequently be united with Jesus in the resurrection. What happened to Christ on a physical plane is applied metaphorically to the believer on a spiritual plane. In tying baptism to the death, burial, and resurrection of Christ, Paul is identifying and associating believers via baptism to Christ in his salvific work. The essence and heart of the gospel upon which believers are saved according to Paul is the death, burial, and resurrection of Jesus (1 Cor 15:14). These are the very three points with which believers are identified with Jesus in baptism. Thus Paul presents baptism first and foremost as an identification of the believer with Jesus in his death, burial, and resurrection. The idea of identity with Jesus in baptism is similarly stressed by Paul in Gal 3:27, ὅσοι γὰρ εἰς Χριστὸν ἐβαπτίσθητε, Χριστὸν ἐνεδύσασθε//”As many of you as were baptized into Christ, you have clothed yourselves with Christ.” The idea of identification in baptism in Gal 3:28 is seen in the metaphor of being clothed with Christ. (Tony Costa, Worship and the Risen Jesus in the Pauline Letters [Studies in Biblical Literature vol. 157; New York: Peter Lang, 2013], 219-220)