At the end of Levush, Orach Chayim, the leniency of the sages of Krakow is brought, permitting the blessing “that joy dwells in His abode” at a mixed-seating gathering. The Levush himself is somewhat ambivalent about the leniency, but Ashkenazi Jews relied on this leniency throughout the generations. According to the Levush’s understanding of the leniency, it is based on the understanding that “white geese” is not only a spiritual level but also a sociological reality. Someone who is accustomed to this—there is no prohibition here. It is part of the public sphere, and this is also what Igrot Moshe says in the responsum about traveling by train: that someone who refrains from riding a train because of modesty concerns needs treatment (and all the more so someone who steals the public sphere from women through segregated buses should be held accountable).
The Levush remained ambivalent, perhaps because of evolutionary psychology, which argues that men and women are not indifferent to one another even in the public sphere, and from here comes their tendency to try to attract the attention of the opposite sex in various ways, including by the handicap principle. Still, it seems like the sages of Krakow, for otherwise you would make life impossible for everyone.

Now that I think about it, it would be worthwhile for the Rabbi to bring the quote from the Levush in the site’s quote section in the sidebar, alongside Rabbi Kook and the Maharal.

It fits the spirit of the site, but it deals with too specific a topic and not with thinking more generally.