This is very much related to the societal norms. R Salanter was very interested in how German Rabonim were able to work with their community, and he was amused at seeing ladies showing up for the lecture of one of them, saying that if he (R Salanter) tried such an event in Lita, he would be put in cherem.
So, there is no simple “halakha” here.
We now live in same countries, but often in different societies. So, each community should follow their reasonable rules without getting crazy in either direction.
I once observed a funny situation: an academic husband gave a lecture to Jewish audience describing some interesting findings that came from his travels around the world. After the lecture, some people complimented his wife for letting him do such exciting work while holding the fort at home. Little did they know that his wife was an even busier professional, and this traveler was actually “holding the fort” all the days he was not on travel.