It's important to make distinctions here...
"Jewish state" does not mean "Judaist" state. "Jew" is not a religious title, it is an ethnic one. Most Jews happen to follow the religion of Judaism, but not all of them.
Although the practical reality is Judaism will have significant influence in a Jewish state as per Zionism, there is nothing in Zionism that specifically requires a religious element. An all-Jewish secular state, or (just going to extremes) an all-Jewish Hindu state would still be Zionist.
-Gumboot
Very true, I can only offer an anecdote but here goes anyway:
I was over in Israel last year, visiting the development centre of one of our software suppliers. Lunch time conversation with some of my Israeli colleagues, I was very surprised to hear one say “We seem to have quite a lot of Jews on this project”. I made a daft quip along the lines “well we are in Israel”. There most certainly is a distinction between ethnic Jews and religious Jews, the majority of the people a came across considered themselves to be ethnically Jewish rather than religiously Jewish.
* - And no I did not perform a scientifically valid poll, with appropriate sample sizes, as I said just an anecdote.