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No. Not all women's movements are feminist. There are actually a handful of anti-feminist women's movements right now, who argue that the feminist movement has been detrimental to women, families, and society.
There are many different kinds of music and bands which have had an effect on the feminist movement. There are bands like Bikini Kill and the Riot Grrrl Movement.
Consider Shakespear's Sister as a pioneering essay in feminist movement
It had undertones of Lesbianism and helped women to transition away from an oppressive patriarchy to Lesbianism.
Feminist movement in America was led (mainly) by Susan B. Anthony.
Several unfair reasons still exist that were not solved by the feminist movement. One of the most egregious is the disparity in pay between men and women.
Technically, all you have to do is identify as a feminist. At worst, you'd be a bad feminist (as opposed to not a real feminist) because feminism is a movement, not an organisation. To be a good feminist, you'd have to engage in women's rights advocacy or women's rights activism.
The most easier way to find information about the feminist movement is on the Internet. The information also can be find on magazines or books which are related to feminism.
Feminism is the movement that supports gender equality. To be a feminist is thus to be someone who thinks that men and women should be equal socially and economically.
To change social patterns of inequality.
The feminist movement is still current, so women want now what they have always wanted: equality. Feminism seeks to give women equal footing socially and economically to men.