My current schedule doesn’t afford me the ability to write long, detailed, researched replies anymore, but I’ll just say that we have first hand accounta of the chofetz chaim literally making fun of rabbi kook’s name when he made his twisted statements about soccer playing mechalelei shabbos being “holy”. He called the pritzus painting artist Rembrandt a “tzadik”. He eschewed eating meat in clear, open violation of the gemara in Nazir which calls a lerson who abstains from devorim mutarin as a sinner, from “asher chatah al hanefesh”.
Rabbi yoshe ber believed compromise was necessary to save Judaism, and that the yeshiva world would crumble into obscurity if we didn’t create a “new talmid chacham”, who can darshen up the new york times. He believed in lowering our standards lf greatness to save us, much like conservatism, minus the outright denial of the Torah. But that is in its own right a denial or ki lo sishakach mipi zar’o, that torah – pure torah – will never be forgotten. He based his idea of odom harishon on kiekeergard. He had no problem attending operas and did nothing to chastise his waywars community.
Your quotes about the state being aschalta degeula come from menachem kasher, who forged signatures, some from rabonim who had already been niftar. Rav ovadia believed those quotes in his teshuva regarding saying halel on 5 iyar. His decision was largely based on that fallacy. Yeshivishe sefardim who are very into rav ovadia do not say hallel on 5 iyar, or omit tachanun; that’s what’s done by sefardim in chazon ovadia mosdos, as well as places like ateret torah in Brooklyn.
Rabbi yoshe ber’s own observance, as rabbi kook’s, was not wavering. They kept halacha (minus the operas, kol ishah is assur), but diverged from the mesorah in dangerous ways that their talmidim only expanded on and completely left normative judaism.
The issue isn’t secular knowledge. That’s a strawman argument. The rishonim who were knowledgeable (most, I’d argue all were) were not influenced by non jewish philosophy any more than they were influenced by Christianity or Islam, though many knew those systems in order to refute them.
Haskalah was a different era with different problems. Rabbi kook and rabbi yoshe ber in their own ways allowed alien, admittedly non torah ideas into their judaism, to differing degrees at different points in their life. Zionism/nationalism, the idea that somethinf besides Torah makes one a Jew, was called outright by rav elchonon in ikvesa demishicha as heresy. Cut and dry apikorsus, not a “machlokes”. If Rav Yaakov knew what we knew about rabbi kook, i highly doubt he would have referred to him as such, but to many he was respected. He was a shem dovor, but was known to some as off. When rav miller said that, was he completely aware of the above? Or was he only aware of zionism and simply believing in a state? Rabbi yoshe ber himself, however, remarked in a published interview that he was not at all impressed with rabbi kook’s “scholastics” as he called it.
Shlomo goren was, at one point, respected to a degree, and so was eliezer melamed until recently. Times change, people change, or reveal who they truly are.