Well, there's a lot to unpack here. You raise some good questions but you've also made some bad assumptions.
Like, for example, that the woman pictured is my feminist sister. She's not. Being a woman does not make you a feminist by default any more than being a man makes you a misogynist or an MRA by default.
Sorry, it doesn't work that way.
What she is, is another woman who also happens to hold political and social beliefs that are harmful to women.
But you're right, we cannot wash our hands of these women, as much as we'd like to.
We're not their keepers, any more than men are the keepers of poorly behaving men. That's another conflation and being their keeper isn't what's being asked for.
There are social tools though, that even other great apes employ, to keep aberrant behavior in check when it becomes too harmful to group cohesion. Things that keep violence inherent to dominance hierarchy in check.
There has to be a net benefit to being a social species or individuals will drift toward solitary lives. Individuals have to have some basic belief that they are safe in the presence of other individuals. If they're not, and other individuals of the group refuse to rally, then to save their own lives, those overly harassed individuals will leave the group or be driven to murder the harasser.
That's what's being asked of men. That you join us women in checking this violence against us that has gotten out of hand. By not normalizing it, refusing to gaslight us about it, teaching young men better social skills --make it a priority, intervening if you have an opportunity and it's safe, down voting misogyny online, being more mindful about where and on what you spend your money, etc. We're talking about mostly little ways and little things that show disapproval that we can all do. We're asking you to get your heads out of the sand about it.
Not being the morality police. People have the right to choose their own conduct; they and they alone are responsible for it.
But the rest of us don't have to go along with it, ignore it, cheer it on, minimalize the harm it does, make it the standard by polularizing it, etc.
In regards to the woman pictured above, or rather those she represents, we are puabing back on them. Pretty hard, especially in regards to TradWife culture that's rising because strategically, your best bet to check these behavioral, anti-social aberrations is with the young.
I find it interesting that you believe dominance hierarchy to be baked in, that we have no choice, but refuse to acknowledge the necessity of behavioral checks that keep it viable. And that if one is baked in, so are the others.