You mentioned that people yell at you calling you a Jew. Are you a Hasidic Jew? How else can someone tell that you are Jewish? I'm surprised that a city like NY that is overrun by Jews would have people screaming anti-semetic remarks.
When I ride my bicycle to synagogue on Shabbat, I wear my yarmulke (even though my Rabbi always tells me that it is against Halachah to ride a bike during shabbat, I do it anyway). Wearing the yarmulke is usually a dead give away for angry New York'ers trying to get the right of way.
Also, the city is not overrun by Jews. For instance, head out into Queens and you have a little bit of everything by way of races and religions. Brooklyn has many Italians, African Americans, Haitians, Non denominational Russians, Hispanics and Irish. The Bronx has more Hispanics and African Americans than any other borough. Staten Island has a mix of African Americans, Italians and Irish. Whereas Manhattan is dependent upon the neighborhood which you find yourself in. In Manhattan, north of 110th street it is mostly Hispanics and African Americans. South of 110th street, you have Italians, Irish, Eastern Europeans, African Americans, Asians, Arabs and a decent population of Jews.
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The yarmulke looks like this:
