No one is saved apart from the Holy Spirit. No child is saved because of the family he /she has been brought up in. This should be made clear at the baptism of the covenant child. The sign of baptism is not a saving ordinance. 

These verses are interesting. Hebrews 6:4-6 “It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, who have tasted the goodness of the word of God and the powers of the coming age, if they fall away, to be brought back to repentance, because to their loss they are crucifying the Son of God all over again and subjecting him to public disgrace.” 

This passage is talking about covenant breakers, children and non-Christian spouses who are not Christians yet have been sheltering under the covenant umbrella of their family. They have seen  the proof of the Gospel yet have rejected. 

The Old Testament makes provision for covenant breakers to be put out of the assembly/ salvation. This command was given to Abraham at the time when circumcision was first instituted. The  male baby who was uncircumcised at 8 days old was considered to be a covenant breaker at that time and was to be put outside the covenant community.

Genesis 17:14: “Any uncircumcised male, who has not been circumcised in the flesh, will be cut off from his people; he has broken my covenant.” Here God’s covenant was not only with Abraham alone but God specifically states that “this is my covenant with you and your descendants after you, the covenant you are to keep”. In fact the sign of the covenant was to be extended to all those in Abraham’s household, whether born or bought with money. The covenant blessing covered all those who were Abraham’s descendants as they obeyed God’s commands. 

The other side of the coin is the prodigal son Luke 15:11-31. A covenant family can work in this way too. In this case a son falls away, lives, acts, thinks and talks like a pagan- for all intents and purposes is a pagan- yet by the grace of God, is brought back to the house of faith. 

What I do know about covenant relationships is that God delights to work within the family, but it is no guarantee. At the same time God also delights to work in the lives of odd bods who have no covenant background to lean on. 

There is much confusion over this issue which is one reason why much of the Church today believe in only adult Baptism. A proper understanding of Covenantal theology would lead to the understanding that a child born to christian parents or even one christian parent has been set aside by God to receive spiritual blessings. These blessings do not guarantee salvation, yet are a real asset towards a person’s salvation. 

There are many anecdotes about how a young man born to a christ household, rejects the faith as a teen yet in moments of crisis remembers the teaching of their youth and returns to the Lord. The Christian life is not a mathematical equation and neither is salvation.