This is not true. It is known that the one who said “Kook Shnook” was not the Chofetz Chaim, and unfortunately, a false version of this story has become widespread. It is well known that Rav Chaim Ozer, Rav Isser Zalman Meltzer, the Netziv, Rav Shlomo Zalman, Rav Elyashiv and many other gedolim respected Rav Kook immensely. While one can question his approach to secular zionism, and follow gedolim who disagreed with him, there is often a Yetzer Hara (seemingly worse today than a hundred years ago) to bash anyone who one does not see eye to eye with. Please see the Netziv in his Hakdama to Bereishis about suspicion of others being tzidokim, apikorsim etc., and the damage such thoughts can cause.
Regardless of his view of the state, the Chazon Ish sent a shaila to Rav Kook a week after his arrival in EY, which provides clear proof that he valued Rav Kook as a talmid chochom. (There is also a verified story about the Chazon Ish standing throughout an address by Rav Kook at the opening of a yeshiva in Bnei Brak.) Let us learn the lessons of Yoma 9b.