Answer

A. In general, I don’t think there is such a thing as “Judaism says something about something.” Jewish law has its own conceptual framework, and there one can find specific statements, but usually not ideology and broad general principles. Those are generally formulated by people based on their own reasoning and on one kind of evidence or another (usually rather weak). Feminism is no exception to this.
B. Feminism too is an umbrella term for several different shades and approaches. As a rule, if there is such a need, then it is certainly legitimate to work on its behalf. In some areas I personally identify with it very strongly, and in others less so. The aspiration for absolute sameness at any price is a harmful foolishness. The assumption that men and women are categorically equal or categorically different is also foolishness (and no, there is no contradiction here). What makes sense as the basis of such a movement is a woman’s right to act and conduct herself according to her own understanding and abilities, without reference to generalizations, whether more or less accurate. And note well: not because all generalizations are false, but because they are irrelevant. There is no reason to make a decision about a particular woman because of a generalization (even a correct one) about women as a whole.