Recognizing that "Gentile" simply means "not quite like us" Mormons call non-Mormons "Gentiles" and Jews call non-Jews "Gentiles". But outside a specific context the word Gentile does not stand on it's own .
For Example: The Lost Sheep of the House of Israel are a unique sub-set of Gentiles who are Israelites, but not Jews. From a Jewish perspective they are Gentiles, but from an Israelite perspective they are not. So when we read:
Matthew 10:5-6 These twelve Jesus sent out and commanded them, saying: "Do not go into the way of the Gentiles , and do not enter a city of the Samaritans . But go rather to the Lost Sheep of The House of Israel."
we need to remember that the Title House of Israel was assigned to the Northern Kingdom when the Davidic Kingdom split. Its members were never Jewish, therefore Jesus command to go first to the Lost Sheep of The House of Israel was NOT a command to go first to lost Jews.
Jesus was both an Israelite and a Jew and what He said here was "do not go to the Israelite Gentiles." (A common misinterpretation has Him talking about Jewish Gentiles .)
The House of Israel later became The Lost Tribes of Israel which won their freedom from the Assyrians ~610 BC. These 5 MILLION Israelites spread quickly to the West and North where they became known to history as The CELTS and later as The Europeans and Americans. It was to these non-Jewish ISRAELITE CELTIC GENTILES in Galatia , etc. that Jesus sent his 12 apostles.
These Northern Kingdom Israelites were not Jews, thus were Gentiles in the Jewish sense. But they were not Gentiles in the Israelite sense because they WERE Israelites. This huge nation of Israelites was simply called the The Lost Sheep of the House of Israel .
These ISRAELITE CELTIC GENTILES made up the bulk of the early Christians, and all the promises they received as Israelites were, and are, still good today. Gods inheritance has no statute of limitations.
That is absolutely false. The lost tribes, if they could be found, would NOT be considered gentiles ("goyim" in Hebrew) according to Jewish law. No descendant of Jacob is a goy. The Ethiopean Jews have been declared (whimsically, perhaps) to be the tribe of Dan and are, therefore, not gentile.
Recognizing that "Gentile" simply means "not quite like us"
I do not know the etymology of the word gentile, but the word Jesus would have actually used would have been "goy," which means any descendant of Noah other than the house of Jacob.
Jesus was both an Israelite and a Jew
I do not understand what you mean by that, other than that all Jews are also Israelites. According the geneologies of Jesus in the New Testament, he was clearly of the house of Judah.
Keep up your good work! You are opening up the Bible and making it understandable.