I spend a lot of time in museum gift shops, and no matter where I might be in the world, I will see Frida Kahlo. Her likeness appears on socks, dolls, puzzles, water bottles, cushions, jewellery, mugs, eggcups, phone cases, shopping bags, votive candles, notebooks, keychains – just about any consumer goods, in fact, that can be formed or printed.

Her face has been reduced to a recognisable shorthand of monobrow, lipstick and extravagant floral headdress (her distinctive upper lip hair seldom makes the cut). Kahlo’s life and career are likewise stripped of detail, with children’s literature and popular art books sanitising her biography, shaping it into an inspiring tale of resilience in the face of physical pain, pride in her identity and art triumphing over adversity. She has been flattened into a beautiful but tragic figure.

Tate Modern’s exhibition, which opened earlier this month, is titled Frida: The Making of an Icon, and indeed her status is now close to that of a secular saint. While I worry that the real, complicated Kahlo – who was sharp-tongued and scandalously rude, a prodigious drug user, heavy drinker, intoxicating flirt and committed communist – has been erased, Beatriz García-Velasco, co-curator of the Tate show, says: “The idea of Frida being universally accessible and inspiring is not something to be apologetic for. It speaks to the extraordinary range of artists and communities she has inspired: Chicana/o art, feminist movements, disability arts, queer culture, and constituencies all over the world who have claimed her as their own.”

The Tate exhibition is not a straightforward survey. Kahlo’s work is shown alongside that of her peers, as well as generations of artists she has inspired. Among them are Rio Yañez, a graphic artist who draws “Ghetto Frida”, a character who has tattoos reading “Diego” at her neck and “Trotsky” at her armpit. “I used Ghetto Frida as a vehicle to satirise Frida’s commercialisation and get my licks in at the art world at the same time,” Yañez has said. A classic print of Kahlo hung on the wall of Yañez’s family’s home in San Francisco’s Bay Area, “as it did in the homes of so many Chicanos, artists, leftists, radical queers and Mexicans”.

The show also examines the wider idea of Fridamania, taking in mass gatherings of Kahlo lookalikes and Camila Fontenele de Miranda’s public portrait project Todos Podem Ser Frida (Everyone Can Be Frida, 2012–20), which invited visitors to cultural events in Brazil to bedeck themselves in embroidered fabrics and floral crowns. “The commercialisation of her image is inseparable from capitalism and consumerism, but it can also be understood as a form of democratic ownership – a way for people everywhere to literally and metaphorically make Frida their own,” says García-Velasco.

Does she not think some of the products emblazoned with the artist’s likeness are a bit … iffy? García-Velasco admits the phenomenon is not “without its contradictions”, citing the widely criticised Frida Barbie released in 2018, which presented the artist (whose mixed heritage included Indigenous roots, and who often used a wheelchair) as a pale-skinned, non-disabled woman with plucked brows.

She sees a “productive tension” between such sanitised mass-market products and “the handmade devotional objects that honour Kahlo as Santa Frida: nichos [devotional dioramas], ex-votos [votive offerings] and calaca [skeleton] figures that all speak to a very different kind of ownership, devotional rather than commercial, and rooted in the communities for whom Frida remains a symbol of resistance and identity”.

The devotion Kahlo inspires is in part because she continues to feel contemporary, whether in her interest in identity or in exploring her life experiences as a woman. Her open portrayals of pain and heartbreak certainly chime with the current vogue for self-revelation. She started painting in her late teens after a bus accident that caused catastrophic injuries to her spine and pelvis. In the early drawing The Accident (1926), she summons a vision of the collision: surrounded by bodies, her own bandaged form on a stretcher in the foreground is looked down on by her floating, disembodied head.

In the courageous painting Henry Ford Hospital (1932) she portrays herself bleeding on a hospital bed after a miscarriage, surrounded by anatomical drawings, machinery and personal emblems. The heartbreak of her turbulent relationship with Diego Rivera is on canvas for all to see. There are grief-charged self-portraits with shorn hair, as well as her brutal portrayal of a literal death by a thousand cuts – A Few Small Nips (1935) – in which a man in a fedora stands coolly over a woman’s mutilated body.

All of this speaks to Tracey Emin, whose work is concurrently on display at Tate Modern. “Women can relate to her” she has said; Kahlo “did images of herself bleeding in the bath, of foetuses coming out of her, and pictures of her family and lovers”. Emin discovered Kahlo as a student and made a painting inspired by the Mexican artist’s portrayal of her family tree. By way of tribute, in 2000, Emin was captured by photographer Mary McCartney in full Frida garb. Recumbent in bed, as Kahlo so often was in a life beset by injury and illness, the portrait now feels like a foreshadowing of Emin’s own illness.

The art is still there, still loved, but to a degree has been transcended by her person. In her lifetime, Kahlo’s art and her constructed identity as a cultural figure emerged as one. Stepping into the public eye at the age of 22 as the wife of Diego Rivera, she turned herself into a character – a queen in a braided crown wearing Aztec beads and traditional tehuana dress – and it is in this guise that she endures.

She has been played by Salma Hayek in a 2002 biopic and appeared as a supporting character in Barbara Kingsolver’s novel of political intolerance The Lacuna. She has even inspired an opera. Earlier this year, the Metropolitan Opera of New York staged El Último Sueño de Frida y Diego by composer Gabriela Lena Frank and librettist Nilo Cruz. The drama is set three years after Kahlo’s death, as she returns to Earth for 24 hours during the Día de Muertos festival: a chance to live for a day without physical pain, and to carry Rivera back to the underworld with her. As Kingsolver has pointed out, Kahlo and Rivera were “two of North America’s first artistic celebrities”.

One of the most important relationships in Kahlo’s life was with the camera. Frida’s father, Guillermo Kahlo, was a photographer; as a child she learned how to pose and perform. It was an early friendship with the Italian-born photographer Tina Modotti that introduced Kahlo to the idea that she might achieve a liberated, modern life as an artist. Meanwhile, her long-term lover Nickolas Muray, a pioneer of colour photography, took up the camera after a career as an Olympic fencer. Kahlo admired him to such a degree that, in one of her many flights of mythomania, she claimed Hungarian-Jewish ancestry for herself to match his own.

In point of fact, Kahlo’s father was German, of Protestant heritage, born Carl Wilhelm Kahlo in Pforzheim in 1871. The artist’s moniker is so familiar to us now that it can be easy to forget that the woman now synonymous with Mexican identity had a German name. It did not escape note during her lifetime: with Hitler in power in the 1930s she sometimes opted instead for her other middle name, Carmen (Kahlo was born Magdalena Carmen Frida Kahlo y Calderón).

Despite frequently painting her own likeness, since her death in 1954, aged 47, popular iconography of Kahlo has derived largely from colour photographs of her by Muray (which are straightforwardly beautiful) rather than her self-portraits (which are often more complicated and painful).

One of the earliest mass-produced objects to bear her likeness was a 1975 silkscreen print by Rupert García titled Frida Kahlo (Septiembre). First printed and sold in San Francisco’s Bay Area, it offered Kahlo as a totemic figure for Chicano communities as they emerged from the civil rights movement of the 60s. (It was this poster that gazed over Yañez growing up.) García based his print on a 1939 photograph by Muray – Frida with Magenta Rebozo – and took the hot pink of the shawl she was wearing as the background colour for his own image.

By the end of the 1970s, Kahlo was taken up by the women’s movement, celebrated as an artist who painted her own reality, whose reputation in life had been eclipsed by her more famous husband. In March 1979, the artist Mary Beth Edelson hosted a party in her New York loft to introduce Ana Mendieta to the city’s feminist art scene. The dress code for the gathering was “come as your favourite artist”, and guests included Louise Bourgeois (who apparently came dressed as herself) and Hannah Wilke. Mendieta dressed as Kahlo: in a photograph of the gathering, she is seated on the floor at the front of the group; her hair braided with ribbons; her eyebrows pencilled into the shape of a hummingbird. Kahlo’s work was still little known and seldom shown internationally at the time.

That changed when, in 1982, feminist theorist Laura Mulvey co-curated an exhibition of Frida Kahlo and Tina Modotti’s work at the Whitechapel Gallery in east London. It was the first survey of Kahlo’s work outside Mexico and its impact was immense: here was a female artist who had been making works about birth, abortion, miscarriage, illness, identity and heartbreak in the 1930s and 40s. The following year saw the publication of Hayden Herrera’s bestselling biography. Together, the book and exhibition unleashed Fridamania. As if to cement Kahlo’s new superstar status, Madonna proclaimed herself a fan, acquiring a handful of paintings.

It is significant that in her posthumous celebrity, Frida the “character” stepped back into the public eye at almost the same moment her paintings finally reached the mass audience they were never afforded in her lifetime. Perhaps more than any other artist, during her life and after it, her art and her persona have come to seem inseparable.

Despite that elevation to modern-day secular canonisation, Kahlo was no saint in real life. Alongside her personal heroism and bold art, it is important to remember that Frida was filled with self-doubt and disappointment in relation to her work, and was capable of treating the people she loved badly. If we expect figures we admire to be pure and flawless, we set ourselves up to fail. If there’s one thing Kahlo’s art reminds us, it is not to shy away from exploring the more complex and difficult parts of life.

Frida: The Making of an Icon is at Tate Modern, London, to 3 January. Hettie Judah is author of Lives of the Artists: Frida Kahlo (Laurence King Publishing).