The actual tshuvot of Rav Kook and Rav Uziel were recently translated into English and published in the Edah Journal. You can find them online with an internet search. (I’d post the link but I want to respect YWN’s policy against outside links.) Rav Uziel shows that women can vote, be elected to public office, be appointed to positions of authority (serarah), and even serve as a judge. Rav Uziel concludes by saying,
“1) A woman has an absolute right of participation in elections
so that she be bound by the collective obligation
to obey the elected officials who govern the nation.
2) A woman may also be elected to public office by the
consent and ordinance of the community.”
Rav Uziel’s opinion, and not that of Rav Kook, is now accepted within Israel.