My current piece is all about this - and almost totally in disagreement with you because ...

Women are fed up of being told HOW and WHEN to do feminism. We're also fed up of men being centered in our fight for equality. It doesn't matter how well-intentioned this is, it's still placing parameters and restrictions on what women do, and how we do it.

Also -

" supporting misogynist narratives can be made into something shameful and weak, they’ll be less likely to do it."

No, many women find themselves the victims of violence when they make men feel like this. We've been taught from an early age to be nice, to smile and do anything to placate men who would be triggered by being made to feel small and weak.