[@Mr Allen J]
Sociology is one thing. Biology, another. Torah and Talmud, the third.

Here's the deal. JUDAISM as a religion and philosophy can be practiced by anyone. This doesn't make a person that is not JEWISH by descent a jew. Who are JEWISH ethnically, by Torah and by blood? Twelve Tribes who made an agreement with Maker when he lifted a mountain over their heads and asked those twelve tribes to be His People. Those are JEWISH people. Membership in these exclusive Chosen People Club is passed on only hereditary, through maternal(AND maybe paternal too, don't remember clearly) side if the jew in question is Cohen, through paternal if any other. 

Next. ONLY a person that is JEWISH ETHNICALLY can ever be JEWISH in religious sense of the word. Only THESE CHOSEN TRIBES have ability and right to serve the Maker as written in Torah and further explained in all Talmud and only they are rewarded and punished properly for good and ill conduct.

ALL OTHER people of different ethnicities, no matter how much effort they make, how many prayers they spoke or how good they know Torah are NEVER JEWISH - they are "Gers" or "virtuous foreigners/outsiders" who merely('merely' is not a most fitting word due to it's particular subtext but I don't have a better one) practice Judaism.

As such a "jewish" ethnicity is a completely viable term seeing as only people of jewish descent genetically can ever be called that.

To put it all in other terms:
"There is only one Jewish ethnicity, despite the fact that people of many ethnicities may practice Judaism. Practicing Judaism and being Jewish are different things and a person of non-Jewish descent that practices Judaism can't ever be called Jewish. As such the word "Jewish" only ever relates to proper genetical jews. Religion of JUDAISM might be practiced by many ethnicities, but there is only one JEWISH ethnicity that"