Health, Rav Kook did not live to see the Medina, but he defended the chalutziim and was maspid Herzl. Rav Tzi Yehuda and Rav Yosef Dov Ber Soloveichik (as well as Rav Aharon Soloveichik)saw the Medina and supported it.
As for being based on kefira, Rav Kook implored frum Jews to make aliya and join the Zionist movement so that the future state would be 100% based on Tora but they did not listen and still are not – in fact, many who do make aliya do not become citizens but stay on “student” or “tourist” visas or only become “permanent residents”. The fault for shortcomings lies squarely on their shoulders.
As for Rav Tzvi Yehuda (Kook), when Yom HaAtzmaut fell on Bahab he said both Hallel and selichot. When asked about it he replied “Hallel on the Medina, selichot on the government”. A Medina is an organism about any government or even form of government. To give one example, France is now on its fifth republic (= fifth constitution) and has had kings and emperors. However, it remains France. Thus, we are joyful at the opportunity generations of our people (including Moshe and Aharon) did not have. We daven to be able to improve it and do our hishtadlut.