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An "apikorsim," would be a Jew by birth, who does not follow his religion. The is why Danny says this...... Reuven is an Orthodox Jew..... not Hasidic.
Apikorsim or apikoros is derived from the word epicureas, a philosepher who believed in simply living life to be happy. In hebrew and other similar languales to make a word plural it would end in either the eem sound or the oat sound like apikorsim (singular apikoros) or kipot (singular kipah). Apikorsim are jews who wouldn't follow the commandments and such. Danny is calling Reuven an apikoros and saying that less observant jews are apikorsim. Since Rueven is orthodox while Danny is hasidic (a much more observant type of judiasim) Danny thinks that Reuven isn't truly jewish, or truly faithful to god.
The Chosen and Wikipedia