Zionism isn’t my qualifier about what makes a gadol. But if someone accepts a non jewish ideology, like rabbi kook, they’re not an authority.
If one embraces something because of suffering and a desire to be redeemed (like the ponevezher rov, tzitz eliezer), they aren’t disqualified from being a posek or even a tzadik, just they haven’t reached the pinnacle of daas torah at which point all negius and bias falls away and only the davar Hashem speaks mitoch grono, ispashtusa demoshe bechol dor. Rav moshe was one such person, as was the chazon ish, brisker rov. the list isn’t very long.