This was discussed almost a century ago and resulted in a big public machloket between Rav Kook z’tz’l, then chief rabbi of Jerusalem, and Rav Uziel z’tz’l, then chief rabbi of Jaffa. Rav Kook was stridently opposed, but Rav Uziel supported, and the rabbinate pretty much accepted Rav Uziel’s position. Religious women have even served in the Knesset.
BTW in many Torah communities it is totally acceptable for women to share their opinions on Torah and secular matters if they are learned.