I think you can clarify the difference between your run of the mill anti-zionist mainstream charedi and a proper anti-zionist like a satmar chassid with the following hypothetical:
If tomorrow Bibi and all the other members of knesset were to do teshuva, put on black kippahs, start consulting with gedolim and only passing laws that were in line with halacha would you still have an issue with the state existing?
From what I understand the minority of poskim such as Reb Yoilish held that creating a state under any circumstances is an issur gamur, whereas rov poskim held the way it was done l’maisah wasn’t allowed (i.e. a secular state founded by a bunch of apikorsim which encouraged droves of yiddin off the derech) but that if a group of rabbanim had founded a halacha state there wouldn’t have been an issur involved.