Interesting, and encouraging, to see this. It clarifies a few things in my belief structure.
I sometimes describe myself as a culturally-Jewish atheist. (Other times I leave off one piece or the other; it depends on the context.) There's a somewhat different term: non-observant, that also describes me -- it means I don't follow any of the rules and don't go to Temple unless somebody I know invites me to something. I know both observant atheists and non-observant theists (and a few people who could be either depending on the phase of the moon -- literally, since Jewish festivals are on a lunar calendar).