Do you believe and teach that the house of Israel were all Jews? I mean that only the Jews were God's chosen people in the Old Testament.
The Israelites were chosen by God above all the other nations because of His love for their ancestors (i.e. Abraham).
"Because He loved your fathers, therefore He chose their descendants after them. And He personally brought you from Egypt by His great power, driving out from before you nations greater and mightier than you, to bring you in and to give you their land for an inheritance, as it is today" (Deuteronomy 4:37-38).
"The LORD did not set His love on you nor choose you because you were more in number than any of the peoples, for you were the fewest of all peoples, but because the LORD loved you and kept the oath which He swore to your forefathers, the LORD brought you out by a mighty hand and redeemed you from the house of slavery, from the hand of Pharaoh king of Egypt" (Deuteronomy 7:7-8).
"Yet on your fathers did the LORD set His affection to love them, and He chose their descendants after them, even you above all peoples, as it is this day" (Deuteronomy 10:15).
This did not preclude other people from being followers of God. Job was not a descendant of Abraham, but he was called righteous by God. "The LORD said to Satan, 'Have you considered My servant Job? For there is no one like him on the earth, a blameless and upright man, fearing God and turning away from evil'" (Job 1:8). Rahab was a Canaanite harlot, yet she is an ancestor of David and Jesus, as was Ruth who was from the country of Moab (Matthew 1:5). Naaman worshipped God, though he was an Armenian (II Kings 5:17).
However, as a nation, God chose the Israelites as the nation through whom He brought salvation to mankind to rescue them from their own sins. That selection did not guarantee the salvation of every Israelite. Instead, most died because of their sins.
I understand that salvation came only by Jesus Christ. The blood of bulls and goats could never take away sins.
Having said that, the people of Israel who obeyed God and died in good standing with God, were they considered saved until Christ shed his blood? And could we say that Israel was basically the church in the Old Testament?
"For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance" (Hebrews 9:15).
Jesus' death covered the sins of those who lived righteously under the first covenant (the Old Law) and well as for those of the future who follow the new covenant.
Israel was a few times referred to as the congregation of Israel (e.g. Exodus 12:13) and God did call them out of Egypt (Hosea 11:1), but generally, Israel was not known as "the called out," which is what the Greek word behind "church" means. What is more common is that both Israel and the church are referred to as the Kingdom of God. See: Receiving the Kingdom.