It took me a while and I needed to move here to get a tiny feeling for the complexity of this issue. Before that, 'jewish' was a label that I had in the same mental box as 'christian', 'muslim', 'hindu' or whatever. Boy is that misleading.
So many things here in Israel are challenging my understanding, every day. It doesn't help that I'd describe myself as agnostic or atheist. I guess Jews are the only example (that I know of) of a group of people that claim to share religion, ancestors and culture. I wouldn't know how - for example - one could create a model of a secular state here. I wouldn't know where to separate culture from religion and I'm convinced that I'll never understand the idea of common ancestry / being descendants of the same tribes.
Maybe this intermingled religion/culture/ethnicity (if this is the right word?) is confusing more people, just like me. And maybe some people react with fear if they don't grasp a concept?