Question or Topic
Was everyone who was "made under the Law" of Moses or old covenant also in the bonds of the new or Abrahamic covenant, by reason of their birth as an Hebrew?
No. This point is clearly expressed by the apostle Paul when he wrote, "For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but In Isaac shall thy seed be called. That is, they which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed." (Romans 9:6-8)
In the generations following Moses', which generation voluntarily chose to come under the old covenant at Sinai (Exodus 24:7), the children of the Israelites were born under the old covenant constitution, or, as it is scripturally expressed, under the law. This was a hereditary covenant by which the entitlement to its blessings and curses was passed on from generation to generation as a matter of fleshly lineage. Thus, it is written of the Lord, that he was made under the law, in common with all the people of Israel. The new or Abrahamic covenant is distinguished from the old covenant in that entitlement to its blessings was not conferred by reason of birth as the natural seed of Abraham.
These "children of the flesh" were not constituted "the children of promise" by the circumstances of their birth. Although literally, with respect to their fleshly lineage, they were "of Israel (Jacob)," they were not necessarily part of the eternal blessings in the line of Abraham, Isaac and Jacob (Israel). What was the essential difference between the two covenants, as it related to Israel after the flesh? The old covenant was an arrangement into which an Israelite was born, according to the law; the new covenant was an arrangement that required faith, as a condition of being joined to it by God. Thus, in Romans 4, the apostle Paul expounds, "For the promise, that he should be heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith; For if they which are of the law [another way of expressing those made or born under the law of Moses] be heirs, faith is made void, and the promise made of none effect." [Romans 4:13,14] It is because of this principle that those of us who were by nature "sinners of the Gentiles" can be adopted as the seed of Abraham through faith in Christ and by obedience to the call of the gospel. [Mark 16:15-16, Ephesians 3:6] In Galatians 3:26-29, the apostle Paul expounds how this relationship as heirs according to the promise is brought about by baptism into Christ.