You know feminism is a cultural force when it’s the subject of celebrity Twitter feuds. But is the kind of white-washed celebrity feminism that makes national headlines worse than no feminism at all?

This week, musicians Nicki Minaj and Taylor Swift had a brief social media spat over the representation of women in music videos. Minaj tweeted her frustration about the lack of recognition she received at MTV’s Video Music Awards, and how black women so often influence the music industry but don’t receive awards or acknowledgment. Minaj, whose Anaconda video was one of this year’s most-watched, tweeted, “If I was a different ‘kind’ of artist, Anaconda would be nominated for best choreo and vid of the year as well.” She followed that with, “When the ‘other’ girls drop a video that breaks records and impacts culture they get that nomination,” and then, “If your video celebrates women with very slim bodies, you will be nominated for vid of the year,” and, finally, “I’m not always confident. Just tired. Black women influence pop culture so much but are rarely rewarded for it.”

For some reason — perhaps because one of her videos featuring a bevy of professional model friends was nominated for a VMA — Taylor Swift thought that was a good time to jump in.

“I’ve done nothing but love & support you. It’s unlike you to pit women against each other. Maybe one of the men took your slot,” Swift wrote.

Minaj responded with understandable confusion, tweeting, “Huh? U must not be reading my tweets. Didn’t say a word about u. I love u just as much. But u should speak on this.” To which Swift said, “If I win, please come up with me!! You’re invited to any stage I’m ever on.”

Swift and Minaj are famous women, so, of course, the immediate media narrative was “catfight,” even though there wasn’t much of a fight — it was a righteously irritated set of tweets by a rap star followed by a series of tone-deaf responses by a pop star. The ante was upped, though, because Swift is a self-identified feminist, and although Minaj doesn’t use the f-word herself, she’s also an exemplar of a kind of Strong Woman ethos that is having a moment in popular culture. And Swift’s response, chiding Minaj not to “pit women against each other,” was the kind of girl-clubby feminism the performer regularly spouts.

The increased relevance of feminism in popular culture is a good thing. That Swift calls herself a feminist and uses her very large platform to spread the gospel of female friendship is great; that  Minaj uses her platform to emphasize her own power and to refuse to let that power be negated by the fact that she likes sex is equally great. But the Swift-Minaj Twitter exchange is a pretty good example of why we shouldn’t turn celebrities into feminist icons.

Swift’s embrace of feminism is fairly new. In 2012, she eschewed the feminist label, saying, “I don’t really think about things as guys versus girls.” Two years later, a friendship with visionary Girls creator and open feminist Lena Dunham shifted Swift’s perspective, and she told the Guardian newspaper, “As a teenager, I didn’t understand that saying you’re a feminist is just saying that you hope women and men will have equal rights and equal opportunities.” Her feminist awakening was international news, and in interviews and public appearances she talked about the importance of female friendship and the value in holding up other women’s work rather than tearing each other down. It dovetailed with her transition into a mainstream pop star from a pop-country princess who sang about boys that often pitted her sweet, innocent self against the cooler, meaner, more sexually experienced young women.

She was in good company, as celebrities from Dunham to Beyoncé to Emma Watson to John Legend have “come out” as feminists in the past few years, opening the door for the famous and not-famous alike to think about gender equality and whether “feminist” is a term that applies to them. And the broader culture has shifted too, with “feminism” becoming increasingly popular as well as socially and politically salient. Feminist writers now grace the pages of mainstream publications, from national newspapers to women’s magazines to Playboy.

And women who come out as feminist are often applauded by women’s publications. Millennial-focused websites will turn your “I’m a feminist” quote into a cute gif with a grammatically awkward “This Celebrity Just Proved How Important Feminism Is” headline, and you’ll make some photo slideshow of 25 Celebrity Feminists. And why not? Praising celebrity feminism is certainly several steps better than This Celebrity Just Proved How Great She Looks In A Crop Top. And if feminism is truly for everyone, then it has to be for celebrities, too.

But there’s a difference between being a feminist and calling yourself a feminist. Feminism is more than just supporting your girlfriends or churning out charming catchphrases about girl power; it’s a political movement, with political aims. Certainly, the feminism of someone like Swift is genuine, but that doesn’t mean it runs particularly deep.

That was in evidence with her tweets at Minaj. “Girl on girl crime,” as many feminists call it — that is, women going after other women instead of focusing on more powerful people or institutions — is a legitimate problem, and one Swift was trying to point to when she told Minaj not to pit women against each other. But Minaj wasn’t doing that — she was going after the power players and the institutions, complaining about MTV’s pattern of rewarding certain kinds of musicians over others. Swift took a superficial understanding of what feminism means — “supporting women” — and superimposed it over a context where it really didn’t fit. And when Minaj pressed her to say something about the systematic exclusion of black women from recognition at awards shows, the best Swift had to offer was “come on stage with me if I win.”

Now, the feminist-minded media is full of rebukes to Swift — she’s everything that’s wrong with white feminism, she’s a faux feminist. In the comments and on Twitter, many also question Minaj as a feminist role model — she’s too sexual, her video was all about objectifying women. What Swift should do is apologize and take this as a basic and valuable lesson in feminism: that even among some of the most fortunate and famous women in the world, “womanhood” is a different experience when you’re a woman of color, and women who deviate from a straight, white, American norm are often sidelined by the same people who claim to be advocates for women generally.

It seems like Swift might be taking that to heart. This morning, she tweeted out an apology for her earlier reaction.*

For the rest of us, maybe the lesson is that, with a handful of exceptions, musicians and other celebrities shouldn’t be feminist role models. They can still be self-identified feminists and powerful advocates for women by speaking about their own experiences and areas of expertise, like Minaj did when she pointed out music industry sexism and racism. They could be even more powerful supporters if they put some of their immense wealth toward the foundations and nonprofits that support women and girls — with women and girls organizations receiving just 7.5 percent of foundation funding, they could certainly use it. As long as celebrities are talking to reporters about feminism, they could throw in a few comments of support for pressing and controversial feminist issues — police killings of black women; the sexual violence in low-income communities, which doesn’t get the same national spotlight as assault on college campuses; ongoing attacks on abortion rights. But they are rarely going to be the kind of thoughtful, nuanced advocates we want. That’s okay, as long as they are willing to lend a hand to the other feminists in this big ecosystem.

Feminism is political. It’s more than a You Go Girl cheer. And while the celebrity cheerleaders are important and can, hopefully, bring more people to the feminist game, the feminist movement itself is one place where they shouldn’t be the stars.

* This post has been updated.