Deuteronomy 4:37-39 says God “chose the offspring” of the Patriarchs, Abraham, Isaac, and Jacob:
And because he loved your fathers and chose their offspring after them and brought you out of Egypt with his own presence, by his great power, 38 driving out before you nations greater and mightier than you, to bring you in, to give you their land for an inheritance, as it is this day, 39 know therefore today, and lay it to your heart, that the LORD is God in heaven above and on the earth beneath; there is no other. (ESV)
God’s having “chose the offspring” of the Patriarchs should not be taken as meaning that every individual born within the covenant is necessarily chosen unto faith and final glory. It is indisputable that some of Abraham’s descendants were finally lost. Rather, God’s “choice” here refers to his decision to formally differentiate the natural offspring of professing believers from that of the world, by granting them outward privileges and responsibilities common to his visible people. The Patriarchal offspring participated in worship, stewarded the divine oracles, and formally inherited the covenant promises (Rom 3:1-2). Yet, at all times, it was necessary for descendants of the Patriarchs to embrace God’s Word by faith in order for the promises to become personally effective for salvation. This two-fold way of relating to the covenant of grace is essentially what Paul is geting at in Rom 3:1-3 and 4:11-12:
What advantage has the Jew? Or what is the value of circumcision? Much in every way. To begin with, the Jews were entrusted with the oracles of God. What if some were unfaithful? Does their faithlessness nullify the faithfulness of God? By no means! […]
The purpose was to make him [Abraham] the father of all who believe […] and to make him the father of the circumcised who are not merely circumcised but who also walk in the footsteps of the faith that our father Abraham had before he was circumcised.
In the same manner, under the New Covenant, God again “chose the offspring” of professing Christians to be counted among his gathered people (Acts 2:39; 1 Cor 7:14). Indeed, Gentile believers are “grafted” into the original tree, symbolizing the covenant community, whose roots go back to Abraham (Rom 4:11). Children of professing believers, as “branches” natural to the church, are therefore to be reared as disciples and heirs of Christ, and comforted with his promises (Eph 6:1, 4). To borrow the language of John’s epistle, covenant offspring are born “among” and considered living members of the church, but only time will tell how many were truly “of” the church, exercising personal faith unto salvation (1 Jn 2:19).
Of course, this presents us with a tension: which of our children really believe? Yet because God “chose the offspring” to participate in covenant life, it is not for believers to exclude their children from fellowship until we see fit to include them. Rather, from birth onward, we must charitably grant our covenant children the benefit of the doubt, or what is better, not doubt their belonging to Christ at all, until—God forbid—we are absolutely forced to do so by the ordinary process of church discipline. Nothing less than an adult rejection of essential doctrines or persistent unrepentant can disassociate our offspring from their natural place within the visible church.