This is a mildly loaded question. Although not as loaded as some on the Zionist left would like to admit.
Generally the Zionist left, and even the Zionist centre and some of the Zionist right (officially at least), don't see the term "Jewish state" as necessitating preference for Jews. It's more incidental. The state is Jewish because Jews live there and are currently constitute a majority. Of course, maintaining that majority requires giving preferences to Jews when it comes to immigration but some would shrug that off as a means to an end or...something.
They try to maintain the Jewish majority.
Orthodox Judaism (the most conservative type of Judaism) holds direct influence over their legal system, deciding who is allowed to get married in Israel, and who counts as a Jew.
Dark-skinned African Jews face discrimination, some even sterilized.
Arab-Israeli citizens face discrimination. Prime Minister Netanyahu, in his most recent re-election campaign, complained about them gaining too much of a voice recently and how horrible that was so vote for him.
Jimmy Cater and others have called it an "apartheid state," like how South Africa was.
There are many other worrying signs.
Israel demands its Muslim/Arab/Persian neighbors recognize it as a "Jewish state," saying it won't sign a peace treaty with any who don't. So it's obviously important to the Israeli government.
I believe in a world where no state gives preferences to religion, ethnicity or any other similar demographic. Like how it legally is now in the United States (though we still have problems with it, our law is on the right side). We support Israel in the United States so much, saying it should be a beacon of hope in the region. But I don't see anything hopeful in a country that declares itself a "(fill in the blank with an ethnicity/religion) state." Israel is one of those. Israel should be better than that. Better integrating all people into Israel as equals under the law would lead to a better chance at peace.