The "Jew" in "Messianic/Christian Jew" and "Hebrew/Jewish Christian" assumes that "Jew" is a term of racial classification. In sharp contrast, "Jew" as in Jewish law and values does not make this assumption (how could it when it not only accepts converts to Judaism, but treats them in all respects as full Jews?).
See how similar the IMJA's concept of "Jew" is to the one produced in Nazi Germany (July, 1933) by the Becker "working team". According to their "Draft Law for the Regulation of the Status of the Jews", 1(1)b, a "Jew" is a person, "whose parents or all grandparents adhered to the Mosaic faith, even if they or some of them later abandoned the Mosaic faith. (e.g. convert to Christianity - my comment)" (2).
It was on the basis of the foregoing "racist" concept of "Jew" (now propagated by racist Christians through associations like the IMJA) that Nazi Germany sent, not only Jews, but Christians also to their deaths in its extermination camps. Even Christians with only one Jewish grandparent were branded as "racial mongrels" by Nazi "race" legislation. They included Christians who, had they not already belonged to a faith other than Judaism, could never have even joined a synagogue! This was the case for one Swedish Lutheran now living in the UK (3). Here is a lady who admits that she never even thought of herself as a "Jew" before the promulgation of Nazi "race" legislation. In terms of Jewish law and values she has never been anything other than a non-Jew. Nevertheless, she qualifies to join the racist Christian IMJA as a "Messianic Jew" or "Hebrew Christian" (i.e. a "Jewish person who believes that Yeshua is the Messiah"). According to the Nazis she was a "mischling" ("mongrel") and a "non-Aryan Christian" whilst according to the IMJA she is a "Messianic Jew" or "Hebrew Christian". A rose by any other name ....
The IMJA grants fellow so-called "non-Jewish Christians" membership thus, "They are welcome as Associate Members, and we value their support. Full members must be children of a Jewish parent, or married to a Jew, otherwise we might lose our primary objective, which is to look after the spiritual and material needs of Jewish individuals who believe in Yeshua" (1).
So no "non-Jewish Christian" in a "racial" sense (if you are still unconvinced, why do you think they ask about parentage?) can have full membership of the IMJA in their own right, but they can have associate membership. This is more usually known as racial segregation (4).
Racial segregation and racial discrimination are common bed fellows. Thus, in accordance with section III, paras. 2 & 5 of its constitution, the IMJA: