Mike Fish: Here is an attempt to answer the question "Who is a Jew"?
“Who is a Jew?” This is an ancient question with no single, timeless answer. On the one hand, being Jewish is a matter of religion – the traditional, matrilineal definition of Jewish identity is founded on halakha (Jewish religious law). On the other hand, being Jewish also may be a matter of ancestry, ethnicity and cultural background. Jews (and non-Jews) may disagree on where to draw the line. Is an adult who has Jewish parents but who considers herself an atheist nevertheless Jewish, by virtue of her lineage? What about someone who has Jewish parents and has converted to Christianity? Or someone who has no known Jewish ancestry but is married to a Jew and has come to think of himself as Jewish, though he has not formally converted to Judaism?
Various people will have their own answers to these questions.
Here are some categorizations:
(1) Jews by religion – people who say their religion is Jewish (and who do not profess any other religion)
(2) Jews of no religion – people who describe themselves (religiously) as atheist, agnostic or nothing in particular, but who have a Jewish parent or were raised Jewish and who still consider themselves Jewish in some way.
(3) Non-Jewish people of Jewish background – people who have a Jewish parent or were raised Jewish but who, today, either have another religion (most are Christian) or say they do not consider themselves Jewish
(4) Non-Jewish people with a Jewish affinity – people who identify with another religion (in most cases, Christianity) or with no religion and who neither have a Jewish parent nor were raised Jewish but who nevertheless consider themselves Jewish in some way. Some say, for example, that they consider themselves partly Jewish because Jesus was Jewish, because “we all come from Abraham” or because they have Jewish friends or relatives.
Mike Fish: Here is an attempt to answer the question "Who is a Jew"?
“Who is a Jew?” This is an ancient question with no single, timeless answer. On the one hand, being Jewish is a matter of religion – the traditional, matrilineal definition of Jewish identity is founded on halakha (Jewish religious law). On the other hand, being Jewish also may be a matter of ancestry, ethnicity and cultural background. Jews (and non-Jews) may disagree on where to draw the line. Is an adult who has Jewish parents but who considers herself an atheist nevertheless Jewish, by virtue of her lineage? What about someone who has Jewish parents and has converted to Christianity? Or someone who has no known Jewish ancestry but is married to a Jew and has come to think of himself as Jewish, though he has not formally converted to Judaism?
Various people will have their own answers to these questions.
Here are some categorizations:
(1) Jews by religion – people who say their religion is Jewish (and who do not profess any other religion)
(2) Jews of no religion – people who describe themselves (religiously) as atheist, agnostic or nothing in particular, but who have a Jewish parent or were raised Jewish and who still consider themselves Jewish in some way.
(3) Non-Jewish people of Jewish background – people who have a Jewish parent or were raised Jewish but who, today, either have another religion (most are Christian) or say they do not consider themselves Jewish
(4) Non-Jewish people with a Jewish affinity – people who identify with another religion (in most cases, Christianity) or with no religion and who neither have a Jewish parent nor were raised Jewish but who nevertheless consider themselves Jewish in some way. Some say, for example, that they consider themselves partly Jewish because Jesus was Jewish, because “we all come from Abraham” or because they have Jewish friends or relatives.
Sources:
(1) Who Is A Jew?: Reflections on History, Religion, and Culture (https://www.jstor.org/stable/j.ctt6wq61q)
(2) Jewish identity and belief (https://www.pewresearch.org/religion/2021/05/11/jewish-identity-and-belief/)
(3) Defining 'Who Is a Jew’ (https://www.haaretz.com/opinion/2013-09-04/ty-article/.premium/defining-who-is-a-jew/0000017f-f723-d460-afff-ff67fa6f0000)
As you can see, answering the question "Who is a Jew" is a complex endeavour with a lot of nuance.