The shield of David is the heraldry of the Jewish people (aka "Hebrews" aka "children of Israel").
The shield of David is not a religious sign in way the cross is --
it is the sign of the "once and future" kingly family of Israel -- much like the Red Dragon of the Welsh.
Jews are a national group and even when they lived as minorities elsewhere, they were for most of history treated as a separate national group --
In fact, the laws of most European countries with respect to Jews are the model for the American relationship with the Native American Nations as "domestic dependent nations"
Israel is the land of "the children of Israel" ie the Jewish land (in the same manner that Ireland is the land of the Irish, Ukraine is the land of the Ukranians, Uzbekistan is the land of the Uzbeks)
(ofcourse, it may be worth noting that many of the allegedly secular nations of Europe have the cross on their flag -- so the use of a religious symbol is not determinitive for the character of the government)
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EDIT -
to your last note --
Israel IS the Jewish country.
That was largely the point behind its establishment in 1920 --
when Turkey was divided among he native populations of the middle east, based on proportional occupation -- one small country was created for the Jews and a massive landmass for the Arabs - about 19 countries most of which are individualy substantialy larger than Israel.
Most countries in the world have a defining nationality and then other minority groups.
Thus,
Ukraine has a large population of Russians and a small population of Turkmen.
Uzbekistan has a large population of Kirghis, and Kirghistan has a large population of Uzbeks...
Russia has something like 70 minority nations.
Likewise Israel is the Jewish country and it has a large population of Arabs, and small populations of Greeks, Armenians, and Cirkessians.