In a comment on my post here, R' Micha expressed surprise at the longevity of the ideologies of Rav Avraham Yitzchak Kook and Rav Zvi Yehuda Kook, given events which occurred after their respective times, which pose challenges to their visions.
I am not expert enough to explain how the ideologies of Rav Kook the elder and the younger would address these realities, although my limited knowledge does suggest that it can be done. To me, the greater point is this: Many people who claim to be "Rav Kookniks" - and I speak of those outside of Israel, for I know less about those in Israel - do not actually have expertise in the thought of Rav Kook. Rather, they are impressed that someone who was as brilliant and Torah-observant as Rav Kook was a supporter of Zionism, worked with the secular chalutzim, and that's good enough for them. Certainly, they won't question Rav Kook's ideology based on new developments; they don't have enough familiarity with that ideology was in the first place.
The same is true within the YU community and its embrace of Rav Soloveichik; many claim to be followers of the Rav, without having heard his shiurim or read his writing.
And, presumably, the same occurs in other sectors of the Jewish world – perhaps with those who claim to follow the Lubavitcher Rebbe, or to be Breslovers, or to follow in the footsteps of Rav Hutner or Rav Moshe. Gedolim are adopted as role models for what they did, not for what they said. [And my use of the loaded term "Gedolim" here is meant to be translated as "role models".]
At first, one might consider this approach benign. A medical student may emulate a physician who is kind and dedicated and conscientious without knowing what motivates that role model. An athlete may imitate some star who has a particular training regimen without knowing the ideas behind it.
But there are risks involved: Consider the medical student who thinks he is emulating the physician, but only because he didn't understand what he was seeing, or where it applied. Consider the athlete who imitates a star without realizing that the star's approach is fine for someone at a later stage in his career, but won't help at his stage. Consider the fan of Rav Shimshon Raphael Hirsch who knows Rav Hirsch talked about the beauty of the Alps, but who doesn't know when Rav Hirsch recommended they be visited and when he recommended one sit in the classroom.
I don't think there is anything malicious in this path of adopting role models without learning more about their ideas. But I do suspect it's dangerous.