As Michael P pointed out -- and I SAID myself in my original post -- this is true. But would those people be singing Shiksa Goddess and the Shmuel Song? No -- the character is written as a white, middle-upper class Jew (like it's composer).
If you want to argue that it shouldn't matter -- that's fine. We can have that debate. But you are completely distorting what I said, and the text of the show.