Re, chofetz chaim and rabbi kook – exterior sources and Kushyos do not dispel historically verifiable accounta. It’s not “the empty wagon”, but rather the father in law of that book ‘s author, rav yerucham gorelick, who was a big talmid of both rhe chofetz chaim and brisker rov, who was also a rosh yeshiva in YU. Not only him, but other talmidim were there at that time and attest to it. The story is common knowledge in South fallsburg, a yeshiva started by rav yerucham ‘s son, rav abba gorelick.
Gil student doesn’t like the story, so he finds ancillary problems with it. “Fun a kasha shtbart min nisht”. The answer to his concerns is clear – the praise of the reshoim was after the agudah conference. The chofetz chaim’s son in law doesn’t speak directly to his father in law’s beliefs, and like I said, gedolim (such as rav hutner which you correctly referenced) changed a lot on both rabbi kook’s ideas and personage. The way you describe rabbi kook as a poetic, blissfully unaware ideological philosopher only serves to further rule him out of the category of gedolei yisroel. Rav elchonon, another great talmid of the chofetz chaim, js quotes in kovetz maamarim as calling rabbi kook a rasha and zionism as avodah zara. That’s no longer a machlokes, that’s an excision of one person and his actions and beliefs from the klal.
Chochma bagoyim doesn’t mean Torah bagotim. Chochma is logic, math, science, and old philosophy. It helps, key word, helps, understand things in Torah, but it doesn’t determine them. The rambam didn’t learn Aristotle until he was a massive gadol with Torah-defined hashkofos, and that’s what he cautions others to do as well in mishneh torah. The kaftor veferach writes that greek philosophy has its origins in torah, and that we’re just taking back what was originally ours. Haskalah was not like that.
Rav Hirsch never used secular studies to define torah; he wrote repeatedly that the chochmos are handmaids to Torah, they serve it, are subordinate to it. Rabbi yoshe ber, while not at the heretical point of torah umadah, where torah is as important as secular studies, still gave it independent importance to a degree.
The fact that rav miller calls rabbi kook a frum jew is telling. Would you call rav Moshe feinstein a “frum jew”? Also, where was that q and a stated?
My main point is that unlike hashkofos themselves, which are gleaned mainly from the words of gedolei yisroel midor dor, attitudes about people are much harder to determine, because people change, are nuanced, and not every gadol knows every detail aboit every controversial figure… believe me, they have more important things to use their mental energies on than if rabbi kook was legitimate or not.
Rather than approach it in terms of “how good/bad was rabbi kook” and quote gedolei yisroel who said kach vekach, a better alternative would be to quote what gedolim say (insert italics) about the issues themselves. What do gedolim say about nationalism(not the state being a salvation, which many gedolim said it was) as an idea, that there is a concept of a jew absent of torah (rabbi kook’s main idea, which he took from European nationalism), look at praising reshoim as an idea and ask – is it ok to praise reshoim? Is it ok to say that Rembrandt was a tzadik? Is it ok to absolve all mechalelei shabbos because they do supposedly holy work building a land they consider no more valuable than Uganda?
Is it ok to say that we need to make compromises to save torah?
Also, re operas…in my yeshiva it is known that rav shraga feivel mendelowitz almost hired rabbi yoshe ber as rosh yeshiva, but conditioned it on 3 tanaim; one of which was to cease attending operas.