Jewish identity FOR the Jewish people has never been determined by "race" and that notion of Jews AS a race is one that was created by Jew haters in the 19th century. Unfortunately it is also a notion that many who don't even recognize it as disrespectful of Jews and have fallen prey to believing it.. despite the fact that Jews have always spoken out that it is a false notion.
My answer is long, but thorough and has reputable references to learn even more.
Jews are a nation people, Israel (tribal origin) bound by an eternal covenant of the faith (religion) of Judaism. It is the laws of Judaism, given by God to the covenant nation, Israel, in the Torah, that determine Jewish identity. It is not a matter of “blood” but of self-determination through the laws of the Jewish people. I know that sounds repetitive but I repeated that because that appears hard for some to grasp.
People related to one another share genetic markers. The Hebrews had no concept of genetics. Jews began as a family, then as a small group of tribes and has remained tribal in nature. However, Jews are NOT considered a race. Jews are not *an* ethnicity. There is simply no *single* Jewish ethnicity. Neither ethnicity or race define Jewish identity. I repeat, it is Jewish law that defines Jewish identity.
We are Klal Yisrael, the community of Israel. . *MANY* different and distinctly Jewish cultures and ethnicities have developed over the millennia in Diaspora lands. The Diaspora refers to the Jewish presence outside of Israel after the destruction of the First and Second Temple periods and the Bar Kochba revolt.
There are many ethnicities that are distinctly Jewish. There are the Mizrahi (from the Middle East and North Africa).The Sephardi (Spanish) and the Ashkenazi, (German, Polish, Russian and other Eastern European), the Beta Yisrael of Ethiopia, and the Cochin of India and others, that are different as to cultural practices and foods, but it is the faith and covenant that binds them all together as Klal Yisrael.
The Jewish people are considered both a nation and a religion. Our connection is primarily one of faith (religion) through the covenant of Israel, yet membership is also conferred by birth, through matrilineal descent. One may also become a part of the nation Israel by adoption of the faith of Judaism and formal procedures of conversion.
One who converts to Judaism is considered as FULLY Jewish as one born Jewish and their children are Jews. This has been the case since the times of the Torah.
However, one may technically be a Jew if their mother is a Jew, but apostate to the covenant of Israel and no longer considered a member of the nation if they leave it for the covenant of faith of another religion.
A few rabbis have suggested that rather than identify the Jewish people as a nation, as the Torah itself calls us directly, we refer to ourselves as “family”..and while that is how we relate to one another, other rabbis say that we should not redefine our identity based on the fact that some people confuse the definition of a nation people, with a nation state, or courtry. Further complicating this detail is the State of Israel. Israelis are citizens of Israel and may or may not be of the covenant nation people, Israel. See important definitions at the bottom.
The Jewish nation began as a group of tribes and our connection to one another is still from the perspective of a tribal nation. (example: as the Lakota nation has tribal procedure and law to determine who is a member of their tribe, who is not, who is expelled and who is adopted, so does Judaism)
One born a member of the tribal covenant nation Israel (Jewish) may not be observant or even believe in God and they’re still a full member, a Jew. They may not be a good member at all or an active member but unless they have voided membership by following something ELSE instead of Judaism, they're still a member, a Jew. An atheist or a secular Jew is not trying to call something ELSE Judaism. That is how one may be an "atheist Jew". Not believing that there is such a thing as deity, any deity is not following a false deity. An atheist Jew may live Jewish ethics and identify with their people, but they did not take on foreign beliefs contradictory to the monotheism of Torah and become “estranged“ from the Jewish people. An atheist may not convert *to* Judaism to become a member of the tribe because an affirmation of faith in the God of Israel is required to JOIN.
Now if one born into the covenant becomes apostate through rejection of the covenant by adoption of another belief contradictory to the covenant, they are still be considered a Jew, but for all intents and purposes, they're not given the status of a member. Their status is "apostate Jew". According to Jewish law they're not counted in a minyan,(the minimum number of adults required for certain prayers and other mitzvot), they can't be buried in a Jewish cemetery, they cannot be given honors to go up to read Torah at a synagogue, and they may not be allowed to speak for the Jewish people. They CAN however, return without formal conversion should they repent of their idolatrous or foreign god worship and then be embraced again as full members. One who has left the Jewish people for the foreign faith of another people must undergo the steps of TESHUVAH , which means repentance and return to the God of Israel. Some groups may require that the individual also requires immersion in the mikveh before being accepted back, but they do not require the formal steps of conversion should the person wish to return.
Jews are in NO way a RACE..other than as members of the human race. Ruth was a member of the Moabite nation that was condemned to be separate from God for their evil. However, she was a righteous woman who converted and adopted the faith of Israel and was the ancestor of King David. The New Testament depicts her as being an ancestor of Jesus, too. I like to bring this up when some Christians want to declare that converts aren't "real Jews" or that Jews are a race. It is Jewish law alone, not Christianity or any other entity that determines the status of who and what is Jewish.
When a Jew adopts a belief that is in conflict with the Jewish religion, the belief does NOT become a " Jewish belief" just because a Jew chooses to believe in it. THAT is the conflict Jews have with the Christians who call themselves Jews if they deceptively try to present their Christian belief AS Judaism. A Jew who converts to Hare Krishna is just as apostate, but there exists no Jews for Hare Krishna or Hare Krishna Judaism evangelical groups spending millions of dollars a year in campaigns to convert secular Jews by convincing them it is a form of Judaism.
You can become a member of a tribe or nation if you meet the criteria of citizenship. And the covenant people, Klal Yisrael, remain as in the earliest days of the covenant..a nation.
Reform Judaism (of which I am a member) will consider as Jewish one whose father is a Jew IF the child was RAISED in Judaism actively and exclusively. Even in Reform Judaism, simply having a Jewish father without exclusively Jewish upbringing, does not make one born a Jew.
Reform Judaism also recognizes that only Orthodox conversion is considered acceptable to all branches.
It is against Jewish law for any Jew to discriminate against a convert to Judaism. Since the time of the Torah converts have been accepted as fully Jewish, and this is the case in all movements. We are not even supposed to refer to the fact that they are converts! It is up to them if they wish to identify themselves as such. They are Jews, period.
The covenant people, Israel have been MULTIRACIAL since the days of Torah, Moses' wife, Zipporah was a black woman. There have been Ethiopian Beta Yisrael since the days of Solomon! And I repeat, one cannot convert to a race. One may convert and become fully Jewish.
The Jewish Bible ( Tanakh ) tells from the beginning book to the end that the righteous of all nations ( Jew or Gentile ) have the capacity to connect directly to God, merit blessing and a place in the world to come. Every human is equal before God according to the Jewish religion. Atonement is directly from God.
To address some who try to claim that "Jews" only refer to one tribe in the Tanakh:
From Megillat Esther (The Book of Esther), Chapter 2
ה אִישׁ יְהוּדִי, הָיָה בְּשׁוּשַׁן הַבִּירָה; וּשְׁמוֹ מָרְדֳּכַי, בֶּן יָאִיר בֶּן-שִׁמְעִי בֶּן-קִישׁ--אִישׁ יְמִינִי. 5 There was a certain Jew in Shushan the castle, whose name was Mordecai the son of Jair the son of Shimei the son of Kish, a Benjamite,
Pretty clear that the Tanach uses the Term Yehudi for all Jews- considering the fact that Mordechai was from the tribe of Benjamin
Shalom