Not sure I understand how Jew can mean nationality. Is this a reference to Israel being a Jewish "state?" Because it isn't. Not only because of the diversity of it's citizens but also because their own laws prevent that as they have never specifically defined Israel as such. That's not to say that there aren't some hard right nationalists pushing for such a law to be ratified, including Netanyahu.
I am intrigued by the concept of a type of "Jewish atheist/agnostic" vs. any other kind of atheist/agnostic. Is it simply a non-belief in the Jewish God? If so, does their disbelief not cover all other Gods for all other religions? That's an interesting concept, imo.