Because the Israelites are the chosen people of God, will they and all the descendants of David be accepted into Heaven even if they do not accept Christ as their personal Savior? They must be living in the will of God and acknowledge him as Lord, the living God, right?
We know and understand that, from the calling of Abraham, God was preparing a people to be holy unto Himself. Holy means that they would be separate from the nations, set apart for God. It was God who raised up Abraham, Isaac, and Jacob to father the nation that would become Israel. These patriarchs were not special, but they were chosen — chosen and given unmerited favor to be God's instrument to bring about His plan and purpose in redeeming mankind.
Being a part of the nation of Israel did not guarantee entrance into Heaven prior to the cross, not does it during this time that we call the church age. Salvation in every dispensation (every time period) has always been by the grace of God through faith in God.
Prior to Jesus' earthly incarnation, the people did not know God's full plan of redemption. They did, however, know that God had promised to send a Rescuer to save them. In the Garden of Eden, God promised a Seed to come (Genesis 3:15) and He confirmed that promise to Abraham, revealing the Seed would come through His line (Genesis 15). It was trusting faith — faith in the God of Abraham, Isaac, and Jacob — that brought salvation of the Lord to the people of Israel prior to the cross.
Hebrews 11, the "Hall of Faith," clearly proclaims that the faith of the Old Testaments saints was in the God who they knew — the God of Promise. This chapter commends the faith of Abel, Enoch, Noah, Abraham and Sara. Verse 6 reminds us that "without faith it is impossible to please [God]: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him." The Old Testament saints pleased God by their faith in Him and His promises, not their works. However, their works were a demonstration of their faith. Verse 13 tells that "These all [the Old Testament saints mentioned] died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth."
They "died in faith" (trusting God), but had not "received the promises" because the promises of God were "afar off" (yet to come), yet these Old Testament saints were "...persuaded of them" — they believed the promises and, more importantly, they believed the God of the promises.