“I think many ehriche Yidden are sympathetic to Zionism even when disagree with something. I saw one such charedi British rav being asked by not-so-observant Yidden whether he is a Zionist, and he replied “yes, in the meaning of hamechazir shechinato l’Zion”.”
This is pathetic and sick. It’s like if someone asks if you’re a Jews for J member then you say, yes, in the meaning of Jew. Zionism is the total opposite of Judaism and, in fact, exists specifically to change Judaism into Zionism and Jews into Zionists. That’s a total conversion, not merely a political club.