Mental examination for admission

Peace and blessings.
I am a 23-year-old man and in recent years I have studied at one of the Hako yeshivahs in the south.
Recently, I have been awakened to the tendency to establish truths through the power of reason and critical thought (which led me to the rabbi's website here and to a certain identification with his views), and as the rabbi probably knows, this is not exactly our style of teaching at Ko.
For a very long time, I wandered within the walls of the yeshiva with sharp criticism of the staff and students, for the fact that the form of study is in fact nothing more than reading very long and very complex lists of what we should believe in, and no one ever stops for a moment and dares to obey the honest demand to examine things in the test of criticism and analysis. (A heartbreaking experience, by the way – being in your home, where until recently you gave your full trust and saw in him honesty, courage, pioneering and heroism, and suddenly all that comes to your mind when you hear his teachings is only criticism and judgment that the people here are shallow and lack the basic maturity to deal with questions that could shake their world).
But on the other hand, I understand that it is inappropriate to try to examine with reason the teachings of Rav Kook, for example, which are all Kabbalah and have nothing real to say there. "The Knesset of Israel was the absolute justice of existence in general," etc. – what can reason say here? How do we approach the study of Rav Kook with this critical reason? It does not seem appropriate to me at all.
All the mind can do is claim that this is an option for the form of reality and that it does not have to be so (not necessarily the sentence I cited, but the entire thought of Rabbi Kook)
Does this mean that Rabbi Kook is irrelevant to people like me?
What am I doing?
It is very important to me not to be ignorant like everyone else and afraid of common sense thinking, but on the other hand, I feel small in my intellect to come and examine the things of one of the greatest thinkers of recent generations who does not at all pretend to be rational in his thinking.
thanks. . .