About the "being perceived as fragile" thing: women are not being offered a walk home because they are fragile, but because they are more valuable than men. Men are in fact more endangered on the street than women, but nobody cares. Does she/he really prefer a life in which nobody cares about her well being?

Also, is it disputed that on average women are physically less strong than men? And even if they were the same on average, suppose the women is pregnant (you can't always know) - should a pregnant woman get into kung fu fights with street thugs? What I mean is: this is not just perception, just reality.

For the second part I also don't have a lot of patience. Just ignore the neighbor and do what you want? You can always find somebody who disagrees with whatever you do, so that can't be a criterion.