Question: "When did the separation of humanity into Jews and Gentiles occur?"
Answer: Although there is no direct mention of the time when the Jews and Gentiles became separated, there are two primary lines of thought. First, some view the separation occurring with the descendants of Adam and Eve. According to this view, the chosen line of Seth was always separate from the rest of humanity. Therefore, Seth’s descendants were considered “Jews,” while the rest of humanity were considered Gentiles. Second, some view the separation of Jews and Gentiles as occurring with Abraham, when God formally chose Abraham to be the father of His chosen nation.
It is clear that there was always a chosen line of ancestry. This is evident from the fact that the Book of Genesis only gives the genealogy of Seth (although Cain’s genealogy is mentioned briefly), ignoring all the other descendants of Adam and Eve. The line of Seth is traced all the way to Noah (Genesis 5), then Abraham (Genesis 11), then the 12 sons of Jacob (Exodus 1), then through the reigns of all the king of Judah (1 and 2 Kings). When we arrive at the time of Jesus, the chosen line of Seth reaches its ultimate goal in the birth of the Messiah (Matthew 1; Luke 3). So, yes, there was always a chosen line, but that does not mean there has always been a separation of Jews and Gentiles. Until the time of Abraham, and then fully outlined in the time of Moses, the chosen line was not commanded not to intermarry with the rest of humanity.
It seems, then, that the formal separation of Jews and Gentiles did not occur until God called Abraham to be the father of His chosen nation, Israel (Genesis 12). Many view Abraham as the first Jew, even though the precise term Jew did not come into use until after the return from exile when the tribe of Judah (“Jew”-dah) was dominant. However, since Abraham’s son Ishmael was not of the chosen line, and since Abraham’s grandson Esau was not of the chosen line, a more accurate placement of the division of Jews from Gentiles would be with Jacob, whose name was changed by God to Israel (Genesis 32:28). All of the descendants of Jacob, through his 12 sons (the fathers of the 12 tribes of Israel), were members of God’s chosen nation. Therefore, it seems most biblically sound to place the division of Jew and Gentile at Jacob, the father of Israel.
What was God’s purpose in separating Jews from Gentiles? God’s desire for the Jews was that they would go and teach the Gentiles about Him. Israel was to be a nation of priests, prophets, and missionaries to the world. God’s intent was for Israel to be a distinct people, a nation who pointed others toward God and His promised provision of a Redeemer, Messiah, and Savior.