mariner,
The disagreement between say Brisk/Satmar/etc. and say the Agudah/etc. whether to participate in the Israeli government organs (i.e. the Kenesset) is a minor one, analogous perhaps to whether to daven sefard or ashkenaz. (Yes, Brisk/Satmar/etc. is vocal in opposition to voting and taking Israeli government money. But this is a minor issue in the grand scheme of things.) In principle they are in agreement in their opposition to (and Agudah/etc. IS officially opposed to) zionism.