As this is a question looking for opinions there will likely be different ones.
Answer 1
Yes, it's a Jewish state.
Answer 2
It depends what is meant by "consider".
Israel, according to its Declaration of Independence, which provides Israel's "Mission Statement" describes Israel as "Jewish and Democratic State". These two terms are in tension with each other. Judaism has a pre-set Halakha or Religious Law that governs conduct in all sorts of daily activities. Halakha treats men and women differently and it treats Jews and non-Jews differently. This is not to say that the view is necessarily right or wrong, but this clearly clashes with the fundamental notions of equality before the law established in its democratic component.
As a result, Israeli lawmakers, whether Jewish or not, should consider Jewish law when debating Israeli policy, since it is part of Israel's Declaration of Independence. However, it should not be the only thing under consideration. Of course, depending on your political leaning within Israel (Hiloni - Secular vs. Dati - Religious) you will argue as to whether the Democratic Law should prevail or whether the Jewish Law should prevail. Personally, I think that allowing Israel to remain more democratic than religious permits Jews who wish to embrace the Torah more fully the option of doing so without forcibly compelling those who do not wish to do so to do that, whereas enforcing Religious Law would have a deleterious effect on the rights of the Non-Religious to stay that way.
To read more about the Israeli political divisions between Secular Israelis and Religious Israelis, please see the Related Question.
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