The United Kingdom is a country of all its citizens and not a country to citizens of other countries who would have automatic rights to the UK based on religious criteria as is with the case of Israel. So when Israel is defined as a Jewish state, it means that it is a state of Jews everywhere unlike other countries who are states of their citizens. Also, citizenship is synomymous with nationality in most countries, but not so in Israel as an "Israeli" nationality does not exist. But a Jewish nationality does. Jews are not a nationality in the UK and neither are Christians, Muslims, etc. Neither does that work that way in the USA. So Israel being a "Jewish" state takes on a meaning that is quite different that what you are trying to present, and what most people do not understand.
Man shot dead in northern Israel town of Bi'ina, police say the murder was gang related (Haaretz)
from the article: The impossible forfeit