In your last paragraph I think I now see your confusion. You want Jewishness to be a "race." It is not, it is a religion first and foremost. I would call Sammy Davis Jr. a Jew without any reservations, and the CCNY professor who converts to Christianity is not a Jew. His grandparents might have been, but he is not. Jewishness really is not a "race", even as vague as that term is. Jews have certain cultural characteristics that serve to group them, which is why the "ethically" Jewish term is useful in conversation, but there is no way that there is a Jewish race.
I understand your statement about it being a religion "first and foremost," but I in no way intended to intimate that it's a racial thing. I don't believe that at all. What I'm speaking towards is the ethnicity of being Jewish. And, of course, ethnicity can encompass all races at once yet remain a true ethnicity.
I would call Sammy Davis Jr. a Jew without any reservations, and the CCNY professor who converts to Christianity is not a Jew. His grandparents might have been, but he is not.
As for the City College professor no longer being of the Jewish faith is correct. But that does not speak towards the professor's ethnicity, which would still be Jewish.
So the fulcrum of your argument is the Jewish faith. But this totally leaves out the ethnic composition which is also valid, is it not? Also, since the Jewish faith is your sticking point, is a Jew who is an atheist still a Jew?
It's very circular in my mind.