The crux of your thesis is that “the actions in which [feminists] take part are, and must be, specific and exclusive to women”.
Your reasoning for this declaration is enshrined in your answer to your query: “what action, in good faith, can a man take to promote [the] aim” of “the establishment and flourishing of women’s identities, cultures, and politics, outside of the patriarchy, leading to women having true existences”?
You spuriously conclude that men can’t perform any such actions, ignoring many possible actions, e.g.:
- Speaking out against those who try to force certain roles upon women based on their sex
- Volunteering for feminist organizations / causes
- Donating money to feminist organizations / causes
- Voting for feminist candidates or propositions
- Supporting friends’ feminist goals
None of the aforementioned actions involve men dictating, or even suggesting, what women should do.
If you applied stringent definitions to abolitionism or suffragism based on logic analogous to yours, then William Lloyd Garrison couldn’t have been an abolitionist or a suffragist because he wasn’t a slave or a women. One need not be a slave to support the abolition of slavery, or a woman to support voting rights for women. Similarly, one need not be a woman to oppose sex-defined roles for women (or for anyone else).
Lastly, I’ll offer a three-part alternate definition of feminism that is that is modeled after your definition, but doesn’t include extraneous restrictions on the sex of feminists, or nebulous terms like “true existence”:
Firstly, and most importantly, feminism is a movement about empowering women. Not about empowering men.
The aim of feminism is not equality between the sexes. It is the establishment and flourishing of women’s own identities, cultures, and politics, without anyone or anything else dictating what those should be (based on their sex).
To achieve this aim, the actions of feminism are performed. Those of us who engage in these actions are feminists.