One reason I'm against religious schools is that they can identify children as [insert religion of your choice]. For instance, I and my siblings were sent to Catholic schools. Our uniforms told people that we were Catholic or at least at a Catholic school. Now, why would anyone need to know that?
While the Nazi method of literally labelling Jews is gross, what gill said about not knowing someone is Jewish unless they told you is true.
I had an Equadorean friend in Oxford. He was not the typical colouring (skin, hair, features, etc) of either descendents of Spanish conquerors or of indigenous South American people. I never said anything about this but wondered what his ancestry was, as you do out of curiosity. One day he told me that his father was of "Spanish Catholic" heritage and his mother "German Jew". I said, "Oh" and nodded as it kind of explained that part of his appearance that seemed north European.
His reaction was: "Is that all?"
Er, yes.
Seems he often got remarks he'd rather not have heard when people heard about the Jewish bit.