What is a Jew?

One of the things we had to do at our CRC registration was fill in a form requesting dogtags. One of the questions therein asked for "religious preference." I figured I shouldn't write "no, thank you," but was stumped beyond that. I mean, I identify as Jewish, but not in the religious sense. So in what sense then? Ethnically? Is Jewish an ethnicity? (What about the Ashkenazi/Sephardi split?) Culturally? -- maybe, but ahead of Jewish culture I'm more attuned to/infused with American, Latin American, Russian, and southern cultures, among others. Maybe just as a part of my identity generally, then, components of which include a certain mentality derived from my parents, a propensity for engaging in the neocon conspiracy to rule the world, etc. Yeah, those are the tickets. But then, why I would I want to self-identify that way on dogtags, tipping off the bad guys that I'm the one they definitely want to behead?

No, for religion I put down "none" -- as directed, actually, for applicants "expressing no religious preference." (But it's not that I don't have a preference, valuing each one equally... oh, whatever.) I just hope the ghost of Thomas Jefferson doesn't scorn me for not being cute and putting "deist."