You are a Jew but not Jew-ish, as Jonathan Miller once described himself ( "Beyond the Fringe"). He once asked the Jewish Chronicle how far back in ancestry do you want to go , in defining a Jew. On the traditional basis he was a Jew and a chimpanzee!
You are not even an 'amphibious Jew' (Miller's description of his own father) , one who accepts some small part of Jewish culture and practices as and when, but does not lead his whole life as a Jew. If challenged, he will say that he is one, but does not otherwise think of himself as anything in particular.
In Judaism, you are a Jew, but not otherwise.