‘There’s nothing wrong with that word: it’s not a dirty word.” Sarah Creed, curator at the Vagina Museum in Camden Market, north London, is ending a story about a gynaecologist friend whose child at nursery was told it was inappropriate to say “vagina”. Obviously I know there is nothing wrong with it. But would I wear a pussy pendant, by the Dutch artist Denise Rosenboom, which are apparently flying off the shelves? Would I have Sam Dawood’s period sculpture in my house? (I can see that this is quite a philistine criterion for appreciating art). Or a model of the vulva, identifying all the parts?

A lot of myths are busted in the opening exhibition, titled Muff Busters, at this new museum: what we tend to call the vagina is actually the vulva, for example. There is only one word that describes the whole kit and it was appropriated some centuries ago as an expletive. Discharge is not effluent, it is a sign of self-cleaning. The hymen is not like a wall that you punch through. Most moderately competent feminist adults will know all this, plus, you know, Google. Which is not to say that it doesn’t need saying; rather, that there is something deeper going on here than the correction of an information deficit.

“I think it’s very much part of this new generation’s experience; it’s very normal to talk about vaginas and vulvas,” says Creed. “It’s great that that ethos exists. I’m an 80s child: even when I was a teenager, it was completely taboo.” I am a 70s child, and likewise. However, Emma LE Rees, author of The Vagina: A Literary and Cultural History, recalls feminism’s second wave: “I’m 50, and I can remember my mum being really open and honest, to the point that I can remember bursting into tears when she told me about menstruation. Because it just sounded so horrible.”

The drive to shroud the female pudenda in a mysterious disgust, to make it unsayable, is centuries old; Rees was driven to write her book, which a male colleague predicted “wouldn’t get recognition, because sometimes even serious research didn’t get recognition”, by chance. She came across a Sheela na gig – carvings of naked women with exaggerated vulvas, dating back to the 12th century – on a church in Kilpeck, Herefordshire. On consulting a 19th-century guide book, she was informed that it was “‘a fool holding his chest open to show his heart’. There’s no way that’s what that figure was,” she says.

Such acts of erasure are unremarkable from that century, or indeed, any other. More interesting is the pendulum swing in feminism: from the consciousness-raising days of the hand mirror and the torch, where examining your own apparatus was a political and communal act (there would have been no more purpose to doing it on your own than there would have been staging your own AA meeting); through that late-20th-century phase when sex was no longer political, because nothing was political. In theory, this was because we were post-postmodern; our biology needed not be our destiny and therefore to go on a journey of awakening through your vulva would have been particularly droll. In practice, that meant vulvas going back in the closet. Today, the full beam of attention has returned and to know yourself anatomically is, again, political. It has become the gateway body part to other conversations. Some of them - period poverty, for instance – are timeless, but reanimated. Others – sex work, trans rights – go to the heart of what divides feminism today.

Exhibits at the Vagina Museum, Camden Town. Photograph: Alecsandra Raluca Dragoi/The Guardian

That is not to say that feminism was not divided in the 60s; it is just that, in the absence of social media, nobody noticed. In the broadcast journalist Emma Barnett’s book Period: It’s About Bloody Time, she pieces together feminism’s relationship with the body. Barnett was, of course, concentrating on periods, rather than the more generic place-periods-come-out-of, but the principles were the same. That early radicalism – Germaine Greer telling women to taste their own periods – was not elaborated by the movement, because there was an equal and opposite force within the same generation of women: the equality wing of feminism.

“What they were doing was trying to get us into the workplace,” says Barnett. So, she says, anatomy was “the last thing you’re going to bring up”. This is one of those obvious-sounding remarks that sets off a lightbulb in your head; when I think of that generation, who were at the vanguard of the fight for professional equality, in both wages and opportunity, it is striking how hard-boiled they so often seemed about all aspects of the female experience. Miscarriage? Suck it up, happens to everyone. Childbirth? Back to work in 17 days. Period pain was for wimps; a vulva was like a PowerPoint display, you should only bring it up if you’re going to use it in the next five minutes. I am not just beefing with my mother, by the way. This was all of them. I’m joking. (I’m not joking).

I loathe all the euphemisms: hoo hoos, vajayjays and lady gardens Emma LE Rees

So the gender-equality movement, whose wellspring was radical emancipation, did a handbrake turn back to pubic taboo when it had to make a choice between being accepted in the workplace now and enjoying a brighter, more open, more accepting tomorrow. It felt as though nobody really mentioned women’s bits seriously again until menstrual activism took off in the mid-00s, with avant-garde writers such as Chella Quint documenting a decade of periods, and the likes of artist Ingrid Berthon-Moine, who created a series of portraits of women using their menstrual blood as lipstick.

What had happened in the interim was the post-postmodern 90s, when a lot of energy was concentrated on overcoming taboos around promiscuity. But there was a contradiction at the core of this: sex itself was a feminist act, especially if it was indiscriminate; yet at the same time, we were extremely closed about female sexual organs, right down to what you called anything, or what anything looked like. “I loathe euphemisms,” Rees says. “Hoo hoos, vajayjays, lady gardens. But I don’t think the word ‘cunt’ can be reclaimed, either.” I agree, but I am interested: I don’t remember any adults using those coy synonyms before the 1990s and the swear word used to be 10 times ruder, friendship-endingly extreme.

But tense silences never last for ever. Even without social media and selfie-awareness – the sense that self-acceptance is integral to one’s brand – we would inevitably have reached something beyond complete vulva omerta. Feminism has been on a whistlestop journey from ignoring the vulva to organising around it, and campaigns to end period poverty – often, like the climate strikes, starting at schools, although some, such as FlowAid, focused on awful deprivations endured by homeless women - make sense, even while I find them depressing. (It is such a failure of political empathy, that we would need such a graphic illustration of what poverty actually means before we can talk about it; but that’s 2019, it’s nobody’s vagina’s fault). Contemporaneously, though, other fissures opened up, notably that of trans rights, in which there are certainly people on both sides who would have you believe that talking about anyone’s anatomy, in any context at all, is an insult; verboten.

Sam Dawood’s models of menstrual cups and a tampon at the Vagina Museum. Photograph: Alecsandra Raluca Dragoi/The Guardian

Creed is comfortable on the territory: “We’re a trans ally, we’re an intersex ally. We’re LGBTQ+ positive. It’s not just women who menstruate,” she says. “Not everybody who has a vagina is a woman.” Her framing is different and it takes me a second to realise why: the current debate is fixated on, mired in even, what you need, physically, to qualify as a woman. Creed flips the perspective to “just because you have a vagina doesn’t mean you have to be a woman”, which lets in the experience of trans men (who, to my knowledge, are pretty much obliterated in the current debate, which is all about women-only spaces and, by inference, intrinsic male violence). This makes the question: “What do you need, biologically, to be who you are?” more complicated and thereby less heated.

There has been a subtler attitude change to the vulva within some parts of feminism, which Creed explains, in precis. “Originally, there was a sense of reclamation: ‘This is mine, and it’s nobody else’s.’ But now, it’s more like: ‘This is mine, and also, I want to share it with you all.’ Not literally.”

There is no reason that this should force the issue of sex work – still considered the pinnacle of male oppression in some quarters but an issue of solidarity for others – but it is unsurprising to me that Creed should bring it up. “Sex work historically was seen as for the pleasure of a man,” she says. “It’s difficult when you start there to build in a woman’s perspective.” It’s a judgment call, of course: you could perfectly easily create a vagina museum and still be anti-sex work. But once you reject the notion of the vagina as a mysterious space, you can no longer make the assumption that it is a site of oppression irrespective of whether or not the owner realises it; in other words, there is no reason not to listen to sex workers.

There is one thing about the vulva that has not changed, where the Vagina Museum explicitly sets out to move things on. Women still feel crap about themselves. “One thing that we look at is labiaplasty,” says Creed. “Between 2002 and 2012, it went up by 500 percent on the NHS.” One of the gynaecologists (and there have been a few) who has supported the museum said she had been working in this area for 20 years, had seen hundreds of labias in her time, and only one that was genuinely anatomically abnormal. So it is really mental distress; people are just so upset with how they look. “Your vulva is like your face,” she continues. “There isn’t one look to go for. There is no ideal. But how can anyone know they’re not an outlier, if they’ve only seen their own?”

Yet alongside all that self-hate, there is a playfulness that, I think, can not be explained by changing politics alone, or even at all; the pussy pendants are flying off the shelves. “Who would wear a decorative vulva round their neck?” the third wave asks. “Who wouldn’t?” the fourth wave replies. All the merch and paraphernalia has this ludic, carefree subtext that the intensity of the 60s and 70s, and the squeamishness that came after it, could never have set out to achieve. You cannot strategise your way to self-acceptance; or maybe they did and it just took a long time.