Throughout the Old Testament we see generational promises made to the Old Testament saints. For instance:
Genesis 17:7-10 ESV And I will establish my covenant between me and you and your offspring after you throughout their generations for an everlasting covenant, to be God to you and to your offspring after you. (8) And I will give to you and to your offspring after you the land of your sojournings, all the land of Canaan, for an everlasting possession, and I will be their God." (9) And God said to Abraham, "As for you, you shall keep my covenant, you and your offspring after you throughout their generations. (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.
Clearly the OT covenant of circumcision was generational, intended not only for Abraham, but for his sons. This is not something that was dependent on the faithfulness of his sons, they were to be circumcised prior to their ability to believe. It was a covenant that was independent of the will of those who entered into it.
Throughout the Exodus, Leviticus, Numbers, and Deuteronomy we see an emphasis on generational blessing and cursing, and a generational expectation. The faith has always been expected to be handed down parent to child, one generation to the next. The very curse in the garden was generational. There are countless examples like Genesis 17:7-10 that we could draw on.
Deuteronomy 7:9 ESV Know therefore that the LORD your God is God, the faithful God who keeps covenant and steadfast love with those who love him and keep his commandments, to a thousand generationsThe idea of generational blessing and cursing is an integral component of our faith. So what does this have to do with Dual Covenants and Replacement Theology? It has everything to do with it. If we affirm (which I do not) Dual Covenants, one for the Church one for Israel, then we will presume the generational blessings belong entirely to Israel whereas the Church enters the covenant individually based on their moment of conversion. I contend that the lack of understanding of the generational nature of God's work on our behalf has given revivalism a foothold and has caused the church to be incredibly individualistic.
If someone asks you, 'How did you come to believe?' it is perfectly acceptable to answer because my parents did and I was raised to believe. That doesn't sit well with most conservative Evangelicals but it sits very well with the scriptural norm. I do not deny that everyone must be converted, and that we all 'generationally' inherit Adam's sinful nature, nonetheless in a very real sense parents are a means of grace to their children and many children are converted well before they are aware that they were lost. Again, I know this will not sit well with many, but why not?
The idea that the Church is blessed in an entirely different way than 'ethnic' Israel is an idea that has destroyed generational Christianity. In the dual covenant scheme, the generational promises apply only to Israel, and Christan's 'get in' one at a time. How does this play out practically? Well for one, kids who have believed and loved the Lord their entire lives are told they aren't 'born-again' and are led down to an altar to be saved... even though they were already redeemed. This happens more than you think. It leaves people looking to their moment of conversion as a source of hope, and not to God's faithfulness to them through their parents, grandparents, and so on. It leaves us feeling helpless as we raise our own children, and even questioning how we are going to manage to get them to have a 'salvation experience' when they have seemed to believe for so long already. People end up looking at the back of their pocket testament to see their date of conversion, instead of celebrating the faithfulness of their parents in bestowing the faith to them from an early age. It even leads to generational disrespect towards those who went before us. Can you see the implications, I am sure there are more. If you can ditch the bogus Dual Covenant notion, and begin applying the generational nature of our faith to the church, many of these problems go away.
I do not believe someone is saved just because their parents are! I believe people are saved because Christ atoned for them on the cross. The reality is that this truth, and the application of this truth to the individual happens through generational means, and through evangelism... not evangelism only.