More than ten years have passed since the OP, so that answers to it will not be expected. But often I read, here and elsewhere, about "Jewish" or "Hebrew" songs, tales, jokes, etc., without the necessary distinctions.

Generally, performers who are not well acquainted with the culture of their particular audience must be very careful. "Jewish" can mean

1. related to Biblical Judaism
2. related to Jewish religion as practiced today
3. written in a language or dialect mainly spoken by Jews (quite a different category!)
4. related to the general culture of a Jewish ethnic/cultural group, e.g. Yiddish-speaking in Ukraine
5. political (directly or implied), usually about the land Israel.

Most songs in (Neo-)Hebrew language are of the last category; there is a high risk to pick the wrong ideology. Note also that a "Hebrew school" can either be a school for religious studies in ancient Hebrew or a school for Israelis - possibly quite secular.