According to DLRSJ 1(1) a "Jew" is a person:
a) who adheres to the Jewish faith,
b) whose parents or all grandparents adhered to the Mosaic faith,
even if they or some of them later abandoned the Mosaic faith,
c) who is a descendant of those named under a) and b) (Ibid., p.42).
DLRSJ 1(2) also ruled that children having one Jewish parent as defined by DLRSJ 1(1) are "half-Jews", "as long as they do not adhere to the Jewish faith" (when they would become "full Jews" in law) (Ibid., p. 42).
The concept "Jew" as actually applied later in Nazi legislation commenced with the definition of "non-Aryan" in the First Implementation Decree of the Law for the Re-establishment of the Professional Civil Service (April 11, 1933). The relevant section reads, "A person who is descended from non-Aryan, especially Jewish, parents or grandparents, is regarded as non-Aryan. It suffices if one parent or grandparents (sic) adhere to the Jewish religion" (Ibid., p. 42).
The definitive definition of "Jew" in Nazi law is found in the First Regulation to the Reich Citizenship Law (FRRCL), section 5, para. 1 - "A Jew is a person who is a descendant of at least three racially fully Jewish grandparents" (November 14, 1935). However, FRRCL, section 2, para. 2 ruled that, "A grandparent is without question fully Jewish if he or she belonged to the Jewish religious community". According to FRRCL, section 5, para. 2(a) a "half-Jew" descended from two fully Jewish grandparents is also regarded as a Jew if, "at the time of the promulgation of the law he belonged to the Jewish religious community or afterwards joined it" (Ibid. pp. 42-43).
Clearly Nazi antisemitism was not based on biological "race" but on
the religion of one's grandparents, parents or in some cases, one's own
religion. The religion in question is, of course, Judaism. This is not
the same as claiming that the Nazis did not think that their antisemitism
was based on "race". It is quite typical of racist "thought" to claim that
a person's culture is determined by his/her "race". Presumably in racist
"thinking" this makes adherence to Judaism a legitimate "marker" of "Jewish
race" membership. It was just this notion that the word "racism" was first
coined to describe in 1933 (Banton, M. "Racial Consciousness", Longman,