My only encounter of "female socialization" is on "gender critical" feminist boards. It is discussed always in terms of "if it wasn't for female socialization, my life would be perfect" and how it's reinforced by "the patriarchy". I agree socialization itself is a neutral term, but "female socializing" is not, in my experience. And regardless, feminism's influence on how "gender socializing" is done in the US, "female socialization" is a net positive with all these hamfisted "girls can be anything" campaigns despite girls doing much better than boys in school and no campaigns to help them and an overall popular culture against being masculine. Either way, I don't think it plays much of a role either way since I think every person is socialized significantly different due to environment.