Many within the Confessional Reformed group will state that due to the New Covenant in Christ – the covenant expanded its scope- including the Gentiles within its fold -and this include their children. So not only does it include the Jews and their children- it also include Gentile believers and their children. They based their argument on the following texts:
Acts 2: 37-41
37 Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?”
38 And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.
39 For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.”
40 And with many other words he bore witness and continued to exhort them, saying, “Save yourselves from this crooked generation.”
41 So those who received his word were baptized, and there were added that day about three thousand souls.
and with this text from Colossians about the parallelism of fleshly circumcision and water baptism:
11 In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ,
12 having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead.
I will not belabor exegeting these texts since others more capable than I have done so and pointed out that both paragraphs talks about baptism based on belief and that circumcision mentioned above is spiritual circumcision.
I will also point out that I am also not against the pastoral concern for children who died during infancy and the need to comfort the believing parents -and why most Reformed parents would rather baptized their infant children than wait for the year of accountability for them to do their profession of faith and be water baptized. Infant baptism doctrine grew at a time where infant deaths and world plagues are endemic.
However, based on my readings on the gospel of John, Matthew and the Galatians epistle pf Paul- I believe that “at the point of discontinuity between the old and new covenants- i.e. it is no longer through the blood lines or fleshly descendant that the covenant flows- but through faith” that the covenant expanded and becomes universal- which means it now includes Gentiles in its compass because precisely there is discontinuity in the principle of man’s blood lines or man’s flesh.
If the New Covenant still continue with the Old principle -it will need to remain under requirements of the Jewish boundary markers. So the overarching principle of ‘by faith’ is very important in the New Covenant of the Lord Jesus Christ. This cannot be minimized since this is also the principle that the Reformation started- Justification by Faith Alone. Not by just salvation by Grace Alone -which Augustine already clearly formulated and experiences before -but as Luther knew first hand- the the faith that believes-is also the faith that assures that Jesus is a present reality in a believer. The following texts makes it plain:
John 1: 11-13
11 He came to his own, and his own people did not receive him.
12 But to all who did receive him, who believed in his name, he gave the right to become children of God,
13 who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
And though in the Abrahamic Covenant it is required that all descendants and within his household should be circumcised:
10 This is my covenant, which you shall keep, between me and you and your offspring after you: Every male among you shall be circumcised.
11 You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you.
12 He who is eight days old among you shall be circumcised. Every male throughout your generations, whether born in your house or bought with your money from any foreigner who is not of your offspring,
13 both he who is born in your house and he who is bought with your money, shall surely be circumcised. So shall my covenant be in your flesh an everlasting covenant.
14 Any uncircumcised male who is not circumcised in the flesh of his foreskin shall be cut off from his people; he has broken my covenant.”
It is different how Apostle Paul applies this in the New Covenant context:
5 Does he who supplies the Spirit to you and works miracles among you do so by works of the law, or by hearing with faith—
6 just as Abraham “believed God, and it was counted to him as righteousness”?
7 Know then that it is those of faith who are the sons of Abraham.
8 And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, “In you shall all the nations be blessed.”
9 So then, those who are of faith are blessed along with Abraham, the man of faith.
The ‘children’ of Abraham considered in the New Covenant are those who are in Christ- those who have faith in Jesus:
25 But now that faith has come, we are no longer under a guardian,
26 for in Christ Jesus you are all sons of God, through faith.
27 For as many of you as were baptized into Christ have put on Christ.
28 There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus.
29 And if you are Christ’s, then you are Abraham’s offspring, heirs according to promise.
Matthew also emphasizes that only by being like children that we can enter the kingdom of heaven -and not like being like a child (chronologically):
2 And calling to him a child, he put him in the midst of them
3 and said, “Truly, I say to you, unless you turn and become like children, you will never enter the kingdom of heaven.
4 Whoever humbles himself like this child is the greatest in the kingdom of heaven.
5 “Whoever receives one such child in my name receives me,
6 but whoever causes one of these little ones who believe in me to sin, it would be better for him to have a great millstone fastened around his neck and to be drowned in the depth of the sea.
10 “See that you do not despise one of these little ones. For I tell you that in heaven their angels always see the face of my Father who is in heaven.
It is so clear -that only a strongly held theological superstructure called -Covenant Theology – that is preventing our Christian and Reformed brethren from seeing the truth.
It is also true that we must be cautious in baptizing just anyone claiming faith in Jesus -before we baptize them-since credible faith with outward works -however minimal, must be seen before such water baptisms are done to them.
Some Reformed brethren will also point out that infant baptisms point more to the the teaching that Grace comes before Faith and that Grace is before time. But this is a misunderstanding of what ‘Grace’ is being taught- Grace among sinners who will turn to Jesus in time. Even with children -there will come a time when they will be conscious of who they will be trusting in their lives. They will trust their parents, their siblings-their next of kin-but they will not trust a stranger. Our responsibility as believing parents is that our children will not treat God and His Son-Jesus as stranger -and ascribe to Him all the good things we have and is receiving. This means a family environment filled with awe and wonder of the Majesty of God. And also an education which is well-informed by the guidance of Scriptures and our Confessions.