Joseph, if the CC said that he was referring to the anti-religious stream. In fact, when a speaker at the first Aguda convention disparaged Rav Kook he walked out in protest. As for gedolim criticizing Rav Kook (@Mlk), what else is new? THe Raavad sharply criticized Rambam and Rambam sharply criticized Rashi (without naming him) for his statement regarding the geniza of Sefer Refuaot. The Maharshal also sharply criticized gedolim. See Chavat Yair Responsa 152 regarding this tendency.
MLK,
1. When Rav Kook made that statement women’s suffrage was very rare. Rav Kook’s points were that he considered it immodest (see Levush, Likutei Minhagim 36 that this is relative to the time and place) and would disrupt shelom bayit (apparently the voting in question was not by secret ballot).
2. I do not know who this Rabbi Shapiro is. If you are talking about the “Kook shmook” libel, I asked an acquaintance of mine who is a talmid of Rav Gorelik. He said that he never heard him say it iand does not believe that he ever said it. It is also inconceivable that the CC, who literally wrote the book, would accept derogatory information and make a comment to others on the basis of a newspaper article. The only possibility is that the CC was dismissing the article. See what his son-in-law Rav Aharon HaKohen had to say (available on-line).
3. What about all the gedolim who supported it? The Netziv, Rav Meir Simcha, Rav Shlomo HaCohen of Vilna, Rav Soloveichik, Rav Shlomo Zalman (BTW, as a bachur he was a regular at Rav Kook’s seuda shelisheet and RK was his mesader kiddushin – Rav Elaishiv said that Rav Kook was a gaon olam and when someone brought the chief editor of the Encyclopedia Talmudit to a din Torah for firing him after he excluded RK from an article RE said that he too would have fired him), etc. In any case, I have already pointed out that we now know that Rav Kook was right. If you cannot be of help in making things better at least stay out of the way.