Gadol, it’s far more than the mesorah “leaning” in that direction; there are clear halachos regarding the appointment of women in community posts. See rambam hilchos melachim 5:1, below:
אין מעמידין אשה במלכות שנאמר עליך מלך ולא מלכה, וכן כל משימות שבישראל אין ממנים בהם אלא איש
“We do not appoint a woman to be a ruler in kingship, as it says “(establish) on yourselves a king,” and not a queen. And similarly all appointments in Yisrael, we only appoint a man ”
Re, not leaving the house; the ideals have not changed, but circumstances have led to the application of different factors. Yes, chazal say women should not leave the house often, codified in the rambam and shu”a
Rambam ishus 13:11
גנאי הוא לאשה שתהא יוצאה תמיד, פעם בחוץ פעם ברחובות. ויש לבעל למנוע אשתו מזה, ולא יניחה לצאת אלא כמו פעם אחת בחודש או פעמיים בחודש, כפי הצורך, שאין יופי לאשה אלא לשבת בזוית ביתה, שכך כתוב כל כבודה בת מלך פנימה,
It is inappropriate for a woman to consistently leave, sometimes outside, sometimes in the street, and the husband should prevent this…
However in today’s era, where women’s domestic responsibilities(which are halachik obligations, to take care of the house and children) often leave them with lots of free time(as well as empty nesters, single girls, etc) This must have been a typo of some sort – mod there’s another issue – chazal say idleness leads to a bigger lack of tznius! Not to mention insanity. So for women to not be outside can be problematic in our time through the lens of chazal, not modern thought.
Re, Israeli government; being involved in the government itself is a b’dieved situation and the gedolim who support being involved in it permit such activity despite the fact that the government is heretical and full of frei people, so dealing with women is just another part of that.
But should it enter your mind to say that nowadays rabbonim would allow women to be more involved in the world due to social changes, see shu”t seridei aish chelek 1 teshuvah 150
מ”מ הסכמנו כולנו, שבחירת הנשים היא נגד מנהג ישראל ונגד המוסר הישראלי בחיי הציבור, שהשתדלו תמיד לשמור על כבודה בת מלך פנימה, שהאשה הישראלית תשמור את ביתה ואת חינוך ילדי’ ואל תהי’ קולנית ויוצאנית, לפזר כוחה ולהרוס צניעותה, ולאבוד את חינה וטעמה על ידי ריב ומדנים פוליטיים וציבוריים”
The seridei aish, who was somewhat zionistic and was “in the middle” of both charedim and religious zionist rabbis, said that a woman being involved in politics and using her abilities for things other than her family and house will ruin her tznius and her chein, applying kol kevudah in this context.
Re, doctors; no one ever said a woman can’t have and be successful at a career of her choice, provided it does not interfere with her halachik obligations to her family. The idea that women used to be a prisoner amd and “now” can be “free” is a non jewish import. Women used to work from home and were sometimes quite successful, so much so that chazal said a woman can declare herself financially independent from her husband if she so chooses, to keep her wages in exchange for not being supported with food from her husband. Where it becomes a problem of heretical feminism is when that becomes an ideal that women should aspire to; it’s not, and rav moshe feinstein clearly writes that such ideas are forbidden.