I am lapping up Mrs America, from the opening 70s graphics and the soundtrack to the portrayal of difficult, clever women strategising to get the equal rights amendment ratified. Cate Blanchett, who plays their opponent, Phyllis Schlafly, with ice-cool precision may make her a little too fabulous (she is Cate Blanchett, after all) because Schlafly was the very kind of person feminists find hard to deal with: a woman who was an out-and-out misogynist, and who ultimately mobilised the Christian right and white supremacist groups who would pave the way for Trump. As ever, this was done in the name of “family values”.

But there is as much joy as there is history in the series. Tracey Ullman is grumpily wonderful as Betty Friedan, a woman who took no prisoners. I know: I had discussions with her. Gloria Steinem (Rose Byrne) is surely less innocent than in this portrayal. She knew she was beautiful, and used it to get what she wanted for the cause.

The story of Shirley Chisholm (the magnificent Uzo Aduba) and her brave, but doomed, presidential bid reminds us that all the conflicts we have now have always been there. Is Chisholm fighting for black people or for women, she is asked at one point, as if that is a choice. Are straight women fighting for lesbians? How do women make coalitions in traditional political structures? What matters more: the purity of principle or the compromise of political power?

When my daughters “did” feminism at school, they would come home and ask me which wave I was. I have never known or seen it in this way. Wave after wave cannot be separated. We crash up against the same shoreline. The tide goes in and it goes out again. We fight the same battles 50 years on.

Just with less groovy outfits.

• Suzanne Moore is a Guardian columnist