In a recent widely read article in the frum press, there was a feature on an educator who started a well known school in NY based on the "philosophy of Rav Kook".
The problem is that the school is coed which Rav Kook held is assur. They also have a heavy diet of secular studies while Rav Kook explicitly taught that in youth one should be taught Torah only and secular studies come after one is filled with Torah.
If it means that the school supports Medinat Yisrael - in Rav Kook's time there was no Medinat Yisrael and thus he never discussed it.
I think what it means is that we are not going to be "right wing" like those black hatters.
Those who know a little about the life of Rav Kook know that he was frummer than frum.