I don’t know if there is any religious significance to the State of Israel. I don’t even know if it’s really a “Jewish state” (I mean, an organization has to be halachic to be Jewish… I wouldn’t consider a reform temple a Jewish institution simply because they call themselves Jewish, are by Jews, and claim to represent Jews).
I celebrate Yom Haatzmaut and say Hallel beleiv malei, not because of the State, but because the government of the Land of Israel (in this case it happens to be the State of Israel) has allowed us to return to our land en masse… and through this government there is more Torah in Eretz Yisroel since the fall of Beitar.
Hodu LaShem ki tov. Me’eis HaShem hayso zos, hi niflas be’eineinu.