Try this instead:
Is the United States a Christian state?
My answer is yes it is. It's Christian in that Christianity is the predominant religion, and the most important of the Christian holy days are official government sanctioned federal holidays.
Does that make non-Christian citizens second class? Well, arguably. They may not have different rights, but if you're a Muslim who wants to celebrate Eid or a Jew who wants to celebrate Yom Kippur, then you have to do that on your own time. You have to arrange it around your secular schedule. It makes it harder to practice your cultural traditions.
Is that enough to warrant second-class citizen status? I don't think most people would say so, but some might.
I can think of a lot of ways in which Israel is a "Jewish" state. From state recognized holidays, being a center of Jewish culture, having Hebrew as an official language, and more. Things that contribute to Israel being a Jewish state without infringing on the rights of the non-Jewish citizens.