I'm aware of the tradition. I don't know that it is much of an indicator.
Genesis 17:12
12 And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which is not of thy seed.
Yes, it is determining factor because Jews by thousands years of tradition get Circumcised in the Foreskin. If you are not Circumcised, you are not a Jew and Unclean. Muslims also have this same Strong Tradition and some Jewish Christian leaning Denominations. The Abrahamic Faiths.
Circumcision
"...Prophylactic circumcision originated in the United Kingdom[c] through the influence of British physician Jonathan Hutchinson in the 1850s.[27] Beyond use in healthcare, circumcision plays a major role in many of the world's cultures and religions. It is among the most important commandments in Judaism.[28][29][30] Restrictions on the Jewish practice have occurred several times in world history, including the Roman Empire under Hadrian and the Seleucid Empire under Antiochus IV, as a means of forceful assimilation and conversion; the latter empire’s restrictions were a major factor in the Maccabean Revolt.[d][28][31][32][33][34] Circumcision has also played a major role in Christian history and theology. Though mainstream Christian denominations maintain a neutral position on routine circumcision, it is widely practiced in many Christian communities.[6][7][35][36][37] Circumcised men are presently estimated to constitute around 38% of the world's population.[9][21][38][39] In religion, the procedure is most common among Muslims and Jews (among whom it is near-universal) and the members of the Coptic, Ethiopian, and Eritrean Orthodox Churches. Circumcision is an integral or established practice for members of these faiths, as well as among Samaritans and Druze. It is also widespread in Australia, Canada, New Zealand, South Korea, the United States, parts of Southeast Asia, and Africa.[5][9][40][41][42][43][44] It is relatively rare for non-religious reasons in Europe, Latin America, parts of Southern Africa, and most of Asia...."
Circumcision - Wikipedia