Not race.
Ethnicity AND culture.
Part of the culture as per the OP is humor but much more of course.
https://www.sbs.com.au/voices/article/how-to-be-a-cultural-jew-i-worship-larry-david-instead-of-god-and-think-bacon-is-delicious/oyp57cr8z
Jews are an ethnoreligious group. So no need to follow the religion to be a Jew if you're a Jew. There are also Jews who are not part of major Jewish ethnicities such as converts, Chinese Jews etc. But most Jews do have the ethnic part.
There is a tribal anthological aspect. A person born of a Jewish mother is a Jew. Period.
https://en.m.wikipedia.org/wiki/Matrilineality_in_Judaism
Different than Islam and Christianity.
BTW, there is only one race. The human race.
There is no scientific basis for different races. But there are ethnicities.
Race is a human construct though and widely accepted as real.
Thus Jew hatred (antisemitism) is a type of racism.