Do you have to be born from the literal ancestry of Abraham to be considered a part of Israel? Let us think about that question a moment.
If a person had to be from the children of Abraham in order to be part of Israel and heirs to the promises given to Abraham that would mean that Adam and Eve were not entitled to those promises. That would stand true for Noah too. As a matter of fact, neither Abraham nor his son Isaac had ever heard of the name Israel, for it was not in existence until God changed Abraham’s grandson's name from Jacob to Israel.
Even after the name Israel was used we find in Jewish history people who were not of Jewish descent becoming a part of Israel. Ruth and Rahab are two very famous gentiles that became a part of Israel. Ruth is an ancestor of King David, as well as of the Messiah. An entire nation called the Gibeonites surrendered to Joshua when the Nation of Israel crossed the Jordan River into the Promised Land. This nation became assimilated into the nation of Israel and became Israelites. So as we can see, Israel has always been considered by God to be anyone who is willing to follow the God that Abraham followed.
In the book of Numbers chapter 15, Moses warned the children of Israel that the person who acts defiantly reviles the Lord and shall be cut off from among his people. In other words, if an Israelite rejected God he lost his privilege of being an Israelite in God’s sight.
Regardless of nationality, God considers as His true Israelites as only those people who love him. It is not birthright that gives us standing with God, the promises to Abraham, and eternal life, but a new heart and a new spirit given to us by God.
Picture originally found here