It seemed like a coup for feminism when Slate, an online magazine, launched a new, women-focused website, Double X, last month. Declaring its dedication to "tackling subjects high and low" in voices that were "unabashedly intellectual without being dry or condescending", Double X burst on to the blogosphere, seemingly ready to tackle the knotty question of what it means - and takes - to be a fully liberated woman today.

Except that, instead of squaring up to the sexual politics of the outside world, the site chose to fight its first battle with one of its own, accusing Jezebel - one of America's biggest and liveliest websites for women - of damaging women, degrading its own writers and betraying the quest for true sexual equality.

Jezebel is a tabloid-style website dedicated to "Celebrity, sex, fashion for women - without airbrushing". Based in the US, it has almost 900,000 readers across the world. Its writers lead divided lives: landing some hard-hitting feminist punches - such as raising funds for the victims of "honour" killings in Basra - while at the same time writing salaciously and candidly about their choice to live lives of unashamed promiscuity.

It was in response to one of these articles that Double X lit the fuse that has set the online global community alight. Under the heading "The trouble with Jezebel: how Jezebel is hurting women", it accused its rival of mistaking self-indulgence for acting in pursuit of a political goal.

Double X columnist Linda Hirshman, also a contributor to the New York Times and the Washington Post, referred to an hour-long television appearance by Tracie Egan, a Jezebel blogger who goes by the moniker "Slut Machine", and Maureen "Moe" Tkacik, in which the two young women refused to engage with a serious discussion about sexual politics and culture. Shrugging off a question about rape and sexual responsibility, Tkacik casually explained why she didn't report her own date rape to the police. "I had better things to do," she said. "Like drinking more."

After the programme, presenter Lizz Winstead explained how shocked she had been by the behaviour of the young women. Writing on her Huffington Post blog, Winstead said: "They do not understand the influence they have over the women who read them, nor do they accept any responsibility as role models for young women who are coming of age searching for lifestyles to emulate."

In last week's article for Double X, Hirshman singled out Egan and Tkacik as "a symptom of the weaknesses in the model of perfect egalitarian sexual freedom". The Jezebel website, she argued, is guilty of promoting the belief that modern-day feminism is simply "doing what feels good to you". In doing so, it uses the language of old-style feminism to betray the movement's ideals.

Hirshman, author of Get to Work: A Manifesto for Women of the World, added: "It's the supposed concern with feminism that makes the site so problematic. The Jezebels are ... a living demonstration of the chaotic possibilities the movement always contained." The writer said that she found the attitudes particularly surprising because they "look a lot like the natural heirs of feminism: young, college-educated, urban (mostly New York), single, hard-working, sexually liberated".

Her accusations have reverberated around the global online community. The Jezebel website has responded with "Who are you calling a bad feminist?", in which Hirshman is decried as creating a "victim-shaming diatribe" and for promoting a feminist philosophy that is deeply sexist. "I have seen misogyny and, most of the time, it looks a lot like the ideology Hirshman has the audacity to call 'feminism'," the article stated.

The argument has become so furious that others have stepped in, with all guns blazing. Speaking to the Observer, Naomi Wolf, author of Give Me Liberty: A Handbook for American Revolutionaries, agrees with Hirshman. "Third-wave feminism is pluralistic, strives to be multi-ethnic, is pro-sex and tolerant of other women's choices," she said. "It has led to an embrace of what was once so politically suspect - the notion that you can be a 'lipstick lesbian' or a 'riot grrrl' [referring to a feminist punk movement that emerged in the 90s] if you want to be, that you can choose your persona and your freedom for yourself.

"But that very individualism, which has been great for feminism's rebranding, is also its weakness: it can be fun and frisky, but too often it's ahistorical and apolitical. As many older feminists justly point out, the world isn't going to change because a lot of young women feel confident and personally empowered, if they don't have grassroots groups or lobbies to advance woman-friendly policies, help break through the glass ceiling, develop decent work-family support structures or solidify real political clout.

"But feminists are in danger if we don't know our history, and a saucy tattoo and a condom do not a revolution make," she added. "The fact is, we know the answers to western women's problems: the way is mapped out, the time for theory is pretty much over. We know the laws and the policies we need to achieve full equality. What we lack is a grassroots movement that will drive the political will. 'Lipstick' or lifestyle feminism won't produce that movement alone."

Julie Bindel, a feminist campaigner and journalist, admitted being infuriated by women like Egan and Tkacik. "Feminism is not the freedom to act like a dickhead," she said. "These women are individualists, not feminists. They are lazy, bone-idle women who have no interest taking part in a political movement for change but are trying to get credibility for their selfish lives by playing identification politics. You can't claim to be a feminist simply because you're a woman."

Sandrine Levêque, campaigns manager at Object, the human rights organisation which challenges the sexual objectification of women in popular culture, agreed. "It's almost like what was seen as sexist 20 years ago has been repackaged as empowerment and liberation for women in the 21st century," she said. "It is difficult to make choices in today's pornified culture which bombards us with the message that raunch culture is where it's at for women in 2009."

Younger feminists, however, are more inclined to be critical of Hirshman. "When it comes to Double X, I think we're just left with questions - is it feminist, or is it not feminist? Why did it host a story blaming another woman for not reporting being raped? What is promiscuity? What does that mean? To me, it speaks of trying to slut-shame women who are having consensual sex as and when they want it," said Jess McCabe, editor of the F Word, a British website that describes itself as feminist.

"There is no such thing as a bad feminist. Feminism is a social justice movement, it is not about chiding other women, or establishing yet another set of standards for women to be judged against. We all mess up - we've all been raised in a sexist, racist, transphobic, heteronormative society, and guess what, that affects our behaviour. We all also differ in terms of what feminism means to us."

Ellie Levenson, author of the forthcoming book The Noughtie Girl's Guide to Feminism, is also critical of Hirshman's definition of "good" and "bad" feminism. "A lot of the criticism against Jezebel is against women being open about their sexual antics," she said. "Feminism is about women choosing how to behave and having the same rights and freedoms to behave badly as men do, so in order to make these choices we need to be able to read about women who have made all kinds of choices."

The main problem with feminism today, added Levenson, is that it has become a word that people don't want to be associated with. "But when you start asking them whether they believe in equal rights for men and women they say, yes, absolutely. So it is the word and not the concept that is the problem."

Leveque agreed. Feminism today is very definitely alive and fiercely kicking. "Just look at the number of feminist groups launching up and down the UK, from the Million Women Rise march in London, from the resurgency of reclaim-the-night marches, from the growth of feminist blogs," she said.

"The tide is slowly growing, and it is badly needed," she added. "Things like the rape conviction rate being so pathetic it is almost non-existent, women's services facing closure and the pay gap actually increasing - there is more of a need for feminist activism than ever."

A movement rich in diversity

• Gloria Steinem, Betty Friedan and Susan Brownmiller defined the revolutionary feminism of the 60s and 70s. They protested at Miss World contests and rejected the stay-at-home role and other aspects of traditional femininity.

• They clashed with the radical feminists, including Andrea Dworkin, Catharine MacKinnon, Mary Daly and Germaine Greer, who believed that women were oppressed by men.

• Then came the "riot grrl" phenomenon of the early 90s and Generation X, who were more likely to talk (very) dirty and less likely to oppose pornography.

• The newest strain is the new/power feminist, epitomised by Naomi Wolf and Natasha Walter, who dislike the image of the strident feminist.

• Then there's pop-feminism/feminism "lite". This is Spice Girls feminism: girl power. Feminism as a fleeting fashion trend. Buffy the Vampire Slayer as a feminist icon.

• Finally, there are post-feminists, who believe feminism is dead. Heroines are Margaret Thatcher and Camille Paglia.

• This article was amended on Tuesday 26 May 2009. We said that McCabe agreed that feminism was alive and fiercely kicking. This should have been attributed to Leveque. This has been corrected.