PATRICK HEALY: Caryn, I’m coming off 18 months covering the presidential campaign, and frankly I’ve been wondering if Mrs. Clinton would ever give a speech like Madonna’s on Friday — calling out sexism in America and the rules that trap women but not men. “If you’re a girl, you have to play the game,” Madonna said. “Don’t have an opinion that’s out of line with the status quo.” Madonna and Mrs. Clinton have been controversial in part because they didn’t play “the game.” It’s easy to forget, amid their celebrity and longevity, that Madonna and Mrs. Clinton were once renegades: speaking out and pursuing power in ways that were considered overly ambitious for women. They fought for equality and respect — and they sought the kind of influence and money and fame that men have. Mrs. Clinton’s place and legacy in our culture is just starting to be considered and debated. But only after her speech yesterday did I start to think about her and Madonna as sisters in arms.

CARYN GANZ: Mrs. Clinton is so buttoned up and Madonna is so, well, unbuttoned, that I think many people have been hesitant to make this connection. And because Madonna has used sexual expressiveness as code for all kinds of liberation, she hasn’t been courted as a political ally. But now that both of them have reached a certain age, the sexism they’ve faced for decades has become something more insidious, paired with ageism.

HEALY: A lot of people don’t see sexism hurting Mrs. Clinton — after all, she won the Democratic nomination — but she and her advisers did. As for the sort of “liberation” that Madonna pioneered, Mrs. Clinton has a complicated relationship with it. She came of age in the era of women’s lib, and yet — to help Bill Clinton’s career in Arkansas — she changed her last name from Rodham to Clinton and got new hairstyles and glasses. And when she was most visibly liberated, including in her hard-charging performances in political debates, she got called “likable enough” by Barack Obama in 2008 and a “nasty woman” by Mr. Trump this fall. Madonna, in her speech Friday, recalled that she got so much abuse after releasing her “Erotica” album and “Sex” book in 1992 that she felt like “the most hated person on the planet.”

GANZ: In a 2008 “Weekend Update” segment about Mrs. Clinton’s initial presidential run, Tina Fey said: “Maybe what bothers me the most is that people say that Hillary is a bitch. Let me say something about that: Yeah, she is.” (Ms. Fey later proclaimed, “Bitch is the new black.”) I thought about this when Madonna put the song “Unapologetic Bitch” on her most recent album, “Rebel Heart,” the record where she started to speak openly about the discrimination she’s faced as a female artist over 55. Madonna has referred to herself in many ways in songs over the years, but she waited until 2015, on her 13th album, to reclaim “bitch.”

HEALY: Mrs. Clinton knew some people used that word about her. Like Madonna, she answered the haters with a strong work ethic. Mrs. Clinton put in 18-hour days, thought deeply about policy, and was a tireless campaigner even if she wasn’t the world’s most natural politician. Madonna is no Adele: She wasn’t born with a once-in-a-generation talent and voice. But she succeeded through work, grit and guts.