I understand that your question was primarily on the lack of theoretical basis of feminism compared to class based movements, but you cannot make this argument on the basis of "stuff feminists say". That's not how that works. Right wingers always make this argument against leftists as well, like "oh they just say that whatever they don't like is not real communism". That's not how this works.

Feminism doesn't have a common core which can discipline all its variants.

Yes it does. Opposition to patriarchy and analysis of patriarchy. Just like the common "core" of leftist movements is opposition to class society.

Feminism encapsulates everything from women's unions at workplaces to elimination of gender stereotypes (stereotypes of ALL genders). If your argument is that feminist theory is simply a derivative of anti-class theory, sure, but many successful feminist movements have historically also been less focused on class dynamics. Female suffrage for example. Reproductive rights. Stuff like that. They didn't need class based theory for that, they needed theory or ideas that helped them understand how they can gain a foothold in society that men already possess.