Salvation comes by faith not family.
...and not by profession either, i.e., a mere uttering of the words "I believe in Jesus."
What basis do we believe our children are elect?
Speaking of the New Covenant in Jeremiah 30 we read: "This is what the LORD says: " 'I will restore the fortunes of Jacob's tents and have compassion on his dwellings; From them will come songs of thanksgiving and the sound of rejoicing. I will add to their numbers, and they will not be decreased; Their children will be as in days of old, and their community will be established before me, Their leader will be one of their own; their ruler will arise from among them" 'So you will be my people, and I will be your God.' "
Talking about the time of the New Covenant Jeremiah says “At that time, saith Jehovah, will I be the God of all the families of Israel, and they shall be my people” (Jer. 31:1).
Again, referring to the times of the New Covenant, the Lord says through Ezekiel in chapter 37: 'My servant David will be king over them, and they will all have one shepherd. They will follow my laws and be careful to keep my decrees. They will live in the land I gave to my servant Jacob, the land where your fathers lived. They and their children and their children's children will live there forever, and David my servant will be their prince forever. I will make a covenant of peace with them.”
Zech 10 reads, "And I shall strengthen the house of Judah, And I shall save the house of Joseph, And I shall bring them back, Because I have had not rejected them. And their heart will be glad as if from wine; Indeed, their children will see it and be glad, Their heart will rejoice in the LORD. "I will whistle for them to gather them together, For I have redeemed them; And they will be as numerous as they were before. "When I scatter them among the peoples, They will remember Me in far countries, And they, with their children, will live and come back.”
In the last book of the Old Testament we read about John the Baptist and part of what his mission entailed: Mal 4:5 "Behold, I am going to send you Elijah the prophet before the coming of the great and terrible day of the LORD. 6 "And he will restore the hearts of the fathers to their children, and the hearts of the children to their fathers.”
And what, according to the New Testament, is the reason for this?: Luke 1:17 "And it is he who will go as a forerunner before Him in the spirit and power of Elijah, to turn the hearts of the fathers back to their children, and the hearts of the children to their fathers, so as to make ready a people prepared for the Lord."
This is in contrast to what would happen to the breakdown between the fathers and children of the Old Covenant because of God’s covenantal curses brought upon them. Ezekiel 5:10 “Therefore in your midst fathers will eat their children, and children will eat their fathers.”
The New Covenant restores the people of God. As Jeremiah had stated -- at that time I will be a God to the families of New Covenant Israel, and that they will be my people. And Zech 10:8-10 "I will whistle for them to gather them, they will remember Me in far countries, And they, with their children, will live and come back.”
The Mother of Jesus applies the Old Testament idea of covenantal succession to her day and every day after that: Luke 2:48 "For He has had regard for the humble state of His bondslave; For behold, from this time on all generations will count me blessed. 49 "For the Mighty One has done great things for me; And holy is His name. 50 "and his mercy is upon generation after generation, toward those who fear Him.”
In Jeremiah 31:33 New Covenant members will have God’s law written upon their heart. Why would this mean a removal of the children of covenant members when Hosea says that because the law was not on the Old Covenant members heart this meant their children were cast off? “Because you have ignored the law of your God, I also will ignore your children”(4:6). Wouldn’t New Covenant Jews, who were familiar with Hosea mind you, at least have asked for clarification if the Apostles had told them that their children were not part of God’s people? “You mean the law is on our heart, but our children are still forgotten!? They don’t, as Jeremiah said, return with us? Please explain!” Perhaps they didn’t ask that because they were too busy having numerous debates about the inclusion of Gentiles. Note that. The New Testament notes numerous heated debates the church had over Gentiles being included among the covenant people. It was unexpected so much so that even the Apostle Peter had to have a private talk with God in order to get with the program. But what did these Jewish Christians do when they found out their own children had been excluded? Surely they debated much more vigorously than they had about the inclusion of the Gentiles, right? If the Jews were debating over the inclusion of the Gentiles, how much more would they have debated the exclusion of their own children? But in the New testament we find utter silence. But, that silence is deafening.