They'll certainly do something, but most people who care about the issue won't like what is done. They may:
Become even more hostile about the subject.
Be even less willing to open the ranks to more women.
Double down on "it's someone else's problem".
Worse, people who currently give a shit and act on that may just... stop. "I support their work and I just get attacked for it, why bother?"
Is it worth having allies who hold their support hostage?
They'll certainly do something, but most people who care about the issue won't like what is done. They may:
Become even more hostile about the subject.
Be even less willing to open the ranks to more women.
Double down on "it's someone else's problem".
Worse, people who currently give a shit and act on that may just... stop. "I support their work and I just get attacked for it, why bother?"