It seems that these responses, i.e., is it safe for women to be out walking or running alone, are similar to black people's descriptions of feeling unsafe. Our racist, sexist society has been built from the ground up to send a strong message, from everywhere, that you (women, black people) ought not to be there, not doing that, and that a violent response is permissible. That needs to be REPLACED, not so much stopped. Yes, all men need to be "nice" but if all they can do is stand by when a Bad Actor is acting up, then we haven't stopped anything. We need to develop a script for not doing this, and for interrupting those who haven't gotten the memo.
This is a time for memetic analysis, like how does society work to automatically attack women and black people? As sexist and racist society is structured to produce acts of targeted violence towards certain people, by their race and gender, once those things and the circumstances are established. Then anybody, then men in the area, are "green-lighted" to deploy violent action memes.
Memetic systems are conservative in nature, and we have old ideas of women aren't supposed to be outside the home, and they aren't supposed to go out unescorted. The violence directed at women who step outside these confines is all part of the system, and in many countries (including the USA) it takes the form of yelling at women, calling them whores, and even rape (1).
Is there more to this? Why does such a system evolve? Women are oppressed, often in exactly the same ways, all over the world, but by no means everywhere, especially if you look at behaviors throughout history.
Interesting contrast with Soviet Russia and the famous WWII sniper, Lyudmila Pavlichenko, who came and toured the USA, during and after WWII and the Battle of Stalingrad, and instead of being praised and recognized for her skill and bravery and astounding contribution to the war effort, American women criticized her for not wearing makeup.
The point being that women in the Soviet Union were fighting alongside men (though in lesser numbers) to save their country. American, Canadian, and British women, for their own part, were building munitions and weapons, vitally supporting the war effort, while Nazi German women stayed home, since Nazi ideology framed German women as being wives and mothers and nothing else.
Of course, Anglo women are kept in the same frame by their societies, too, but there was obviously some flexibility which Americans and the allies were able to capitalize on. Germans were stuck until "total war" (totaler Krieg) was adopted, whereupon women entered the workforce to produce munitions, but very late in the game.
Once Americans came back from the war, American women were bamboozled into believing that they were incapably of doing anything than being barefoot and pregnant in the newly built kitchens of the New Suburbia. Of course, many women were keen to carry on working in factories and elsewhere.
It seems that something similar, i.e., a reworking of the role of women in society, to what was done in WWII is called for now. Also examining the role of women earlier in our country's history might shed light. Was calling women whores or harassing them when they were out and about when they were working in factories during WWII? Did this ever happen? Was this nipped in the bud, and if so, how?
(1) How rape figures in to the support of the system, I guess it's not so unclear. Is it a "reward" to the men (and others) participating for supporting the oppressive memes? The question is whether memetic systems support themselves that way, i.e., if you take part in the system, you get some kind of reward, e.g., food, sexual access to some unwilling victim, as opposed to just getting the rewards of support by the cohort, i.e., supporting memetic deployments or lack of immunomemetic deployments which one would otherwise expect when committing an antisocial act, e.g., assaulting somebody.