But "Jew" originally meant "of the tribe of Judah." Jesus was certainly that. Indeed, He is called the Lion of the tribe of Judah:
NKJV Rev 5:5 But one of the elders said to me, "Do not weep. Behold, the Lion of the tribe of Judah, the Root of David, has prevailed to open the scroll and to loose its seven seals."
The nation that formed in Palestine after the Babylonian captivity of the southern kingdom was initially made up of people from the tribes of Judah and Benjamin, along with some Levites. They settled in two regions, with the Judahites primarily in Judea and with Benjamin in Galilee. Internally they are referred to as Judeans and Galileans in the New Testament. The Judeans of the region of Judea came to include all the people living there, regardless of their racial origins. All these people are referred to by translators as "Jews" because they were “of Judea”. But this does not mean “of Judah” only. Included in the population were many descendants of Esau [Edomites]; these subsequently came to control the temple, and these were the leaders whom Jesus said could not hear [and understand] His words.
This is the view of modern Jewish authorities, Encyclopaedia Judaica 1971, 10, 21:
From the division of Israel and Judah, the term 'Yehudi' applied to
all the residents of the Southern Kingdom, irrespective of tribal status.
The words “Jews” and “Judean” did not apply to the Northern Kingdom. They never have!
In the New Testament we have two different words rendered as Jews:
Ioudas – Of the descendants of Judah
Ioudaios - Belonging to Jehudah or of Judea (in the sense of as a country)
Ioudaios is the Greek equivalent of the Hebrew Yehudi. It is translated as “Jew” and includes proselytes to Judaism. This is thus more a matter of being a Jew by religion or region than by race.
Thus we can see that the generalisation of the word Jew cannot be sustained in Scripture. One Greek word covers all the peoples occupying the former land of the covenant people, while the other word covers the covenant House of Judah in isolation. Ioudaios does not specifically refer to race at all and usually refers to people who are not of the descendants of Judah. This does not mean to say that there were no Ioudas [Judahites] or members of other tribes amongst them. From all this we can see that Jew and Judah are not synonymous terms and that there is a sharp distinction between them. It follows that the name, Israel, should not be applied to the Jewish people as a whole or to the country they occupy.
Historically, in the land of Judea, in addition to Judahites, there were Canaanites, Edomites and others, all of whom were proselytes to the Jewish religion. As a consequence, these were labelled “Jews” since they were “Jews” by religion and they lived in the land of Judea. But they were not of the descendants of Judah!
The territorial term explains how Paul could be called a Jew. Paul was a Benjamite [Philippians 3:5]. Paul and eleven of the disciples did not descend from the Tribe of Judah. To help with understanding here, it must be pointed out that the word 'Ioudaios' can cover a mixture of races which may include some of Ioudas, both of which were in the territory of Judea. In the New Testament, the words translated as "the Jews” are used in a bad sense, whereas today they are commonly used in a good sense. Jesus continually condemned "the Jews” [plural], as did the Apostle Paul. “The Jew” [singular] as used in Romans is used in a different sense.
THOSE WHO SAY THEY ARE JEWS BUT ARE NOT
Jesus says here, as well as in Revelation 3:9, that the Jews were liars. If we took "Jew" to refer to Israelites, we have to come to a decision about, them which say they are Jews but do lie [Rev 3:9]. Do false "Jews" [as translated] exist or not? Why should the churches continue to teach that "The Jews" must never be condemned because they are God's chosen race? Did Jesus condemn this section of the Judean nation, or not? This matter is of huge importance as a matter of fundamental understanding. It has a great bearing on prophetic interpretation. It has a bearing upon what is going on in the Israeli state today. This is no minor doctrinal point! Incidentally, "The Jews" are never called God's chosen people in the Bible!
At face value, the translation is saying that there are people who say that they are Jews but who are not Jews in fact. The common acceptance of the word "Jew" says every Jew, regardless of race, is a good Jew and that everyone who says that he is a Jew is a Jew. Jesus is contradicting this.
Are we to agree with Jesus or with Church/Christian tradition?
