The American Association of University Women, National Women Law Students Organization & Ninety-Nines are organizations providing women-exclusive scholarships in academics, law & avionics respectively. I was able to find one article from 2003 that suggested a male-equivalent scholarship for male nurses, but it seems no organization has risen to the role - at least I can't find any so far.
The National Organization for Women, Women's International League for Peace and Freedom & Women's Refugee Commission are primarily political organizations. Notable activities might include, monitoring the UN resolution 1325 which calls upon all parties in conflict to take special measures to protect women and girls from violence in armed conflict (Women's International League for Peace and Freedom) and advocating for legislation and policy that would ensure the safety and well-being of migrant women (Women's Refugee Commission). Out of these, NOW seems to be the most politically active and the most influential in regards to legislation on both state & federal levels, ranging from divorce laws (Apposing the Shared Parenting Act) to wage laws (Promoting the Lilly Ledbetter Fair Pay Act). The MRA is probably closest to the male equivalent of NOW.
There are other organization who also identify as feminist, but it doesn't seem to be their main focus of activities, such as organizations promoting LGBT rights, organizations promoting development in areas dominated by ethnic communities like latino & black americans, etc. I was trying to more clearly define "mainstream feminist movement". There are also several organizations on both sides of the abortion debate, taking either stance as a feminist agenda (Both pro-choice and pro-life organisations).