How do Lutherans fit that bill, considering that they are as concerned to have their newborns baptized as Catholics are??
That's what I said. So are Presbyterians, and Catholics and Anglicans and all other denominations that practice 'infant baptism' (although infant baptism is a misnomer, because they do not just baptize 'infants'; 'family baptism' is a better description because you all believe in baptizing the entire family of the saved person.)
Acts 2:37 Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, “Brethren, what shall we do?” 38 Peter said to them, “Repent, and each of you be baptized 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 your children and for all who are far off, as many as the Lord our God will call to Himself.”
Those who choose to baptize infants real "For the promise is for you and your children" as 'the promise of baptism is for you and your children' and view it as something to be claimed ASAP. In the WCF and the Presbyterian Church this is explained as Acts 2 initiating a New Covenant in the same manner that Genesis (Abraham) initiated an Old Covenant. In the Old Covenant between God and His people, God chose Circumcision as the sign of being one of the covenant people. In the New Covenant, God has chosen baptism as the sign of the covenant. Thus baptizing a baby is not about recognizing that that baby has repented and believed (we have no way to know one way or another what a baby believes), but rather that the baby has entered into the Covenant relationship with God. The baby is part of the visible Church.
Baptists and others who advocate a 'believers baptism' read "For the promise is for you and your children" as 'God will offer your children the same chance at salvation that he has offered you. Calvinists take that to mean that God will choose those children that He will choose. Arminians believe that the child will grow up to choose on his own. The critical point is that those who practice 'believers baptism' believe that the New Covenant Church is made only of those who have believed and repented and been baptized (although many would argue that it is the baptism of the Holy Spirit that saves and the water baptism is done as an act of obedience ... part of sanctification, not justification.)
My point was that the verse 1 Corinthians 7:14 [For the unbelieving husband is sanctified through his wife, and the unbelieving wife is sanctified through her believing husband; for otherwise your children are unclean, but now they are holy.] can be interpreted in claiming "your children ... are holy (set apart)" as supporting the family Covenant view held by all those who baptize babies. [That is why you baptize babies ... because you believe that the entire family, including babies, is part of the New Covenant Church].