The German city of Weimar has long bathed in its historic cultural heritage, boasting such illustrious former residents as Goethe, Schiller, Bach and Liszt. Its quiet cobbled streets are lined with creamy stuccoed piles where great men of letters convened, and stately theatres where premieres were performed. But, while it is happy to wallow in the völkisch annals of its distant past, the city has never much cared for the fact that it spawned the most influential art school of the 20th century, perhaps of all time.

“People here are still a bit unsure about the Bauhaus,” says Wolfgang Holler, museum director of the Klassik Stiftung Weimar, the city’s foundation for classical heritage, which has opened a new Bauhaus museum to mark the school’s centenary. “It is still very much a backward-looking place.”

One hundred years after the Bauhaus was founded here, Weimar has come to terms with it just enough to allow a museum to be built. The small town of Dessau, where the radical school was forced to move in 1925, still boasts the dazzling white studio buildings designed by its founding director, Walter Gropius, while Berlin, where it moved again in 1932, has the Gropius-designed Bauhaus Archive. Both have (delayed) buildings in the works to mark the centenary.

Walter Gropius’s Bauhaus building in Dessau. Photograph: Tillmann Franzen

But Weimar, which remains a stronghold of the conservative forces that originally pushed the school out, has only ever had a paltry display tucked away in a poky space – until now.

Standing as a chiselled concrete bunker on the edge of a new public square, the €27m (£23m) Bauhaus Museum is a stark arrival. It presents a windowless frontage to the square, exuding the austere presence of a memorial, a mute grey block that might not seem out of place at the Buchenwald concentration camp nearby. Some locals have even compared it to the Wolf’s Lair, Hitler’s eastern front headquarters.

Architect Heike Hanada. Photograph: Ulrike Schamoni/Heike Hanada Laboratory of Art and Architecture

“It was important to express Weimar’s ambivalent relationship with modernism,” says the museum’s architect, Heike Hanada, who studied and taught at Bauhaus University in Weimar, and won the project in an anonymous international competition in 2012, having built nothing else before. “It also had to respond to the politically charged site.”

The museum stands next to the Gauforum, a puffed-up administrative complex built by the Nazis in the 1930s as the headquarters of their slave-labour programme. Its central courtyard, originally named Adolf-Hitler-Platz, remains fenced-off to prevent neo-Nazi gatherings from occupying the space – a very real threat in a city where the far-right party Alternative für Deutschland is poised to make strong gains in forthcoming elections. As a blunt grey block inscribed with horizontal strata, Hanada’s building has eerie echoes of the Gauforum’s stone tower, designed to the directions of Hitler himself. “Unfortunately, he was not so bad at architecture,” she says, although she insists that any similarity is a coincidence.

The Third Reich may have been interested in the monumental power of a particularly steroidal kind of classicism, but it had no time for the avant-garde work of the Bauhaus, labelling its output “degenerate” and finally closing the school in 1933. The museum’s sombre character is strangely fitting: it is a mausoleum for a school of thought that Weimar once did its best to eradicate.

Subdued container … Hanada’s Bauhaus Museum – with Hitler’s Gauforum tower in the background. Photograph: Sean Gallup/Getty Images

The subdued container is, thankfully, enlivened by the colourful stories found within it. History has done its best to normalise the Bauhaus, straightening it out as a pure, modernist bastion of form follows function, but the truth is it was a weird, riotously plural place, particularly in its early years. The Bauhaus Weimar period, from 1919-25, is by far the most strange and untold of the school’s history, so this museum fills a welcome and fascinating gap.

The exhibition begins by introducing the range of oddballs and eccentrics who made up the school’s initial teaching staff, alongside a rich range of work their students produced. We meet Gertrud Grunow, who taught classes in “harmonisation”, rhythmic gymnastics where students learned how to relate colours to certain sounds, movements and materials. “You close your eyes and, after a short period of inner reflection, you receive an instruction,” wrote an observer of her class, “either to imagine a certain colour ball and to feel it by penetrating it with your hands, or to concentrate on a note played at the piano. In less than no time, almost everyone is fully in motion.”

Johannes Itten … ‘demonic’ tutor.

Grunow was recruited by Johannes Itten, a primary school teacher-turned-painter Gropius hired to run the preliminary Vorkurs, a compulsory six-month programme for new students. A shaven-headed mystic who wore his own special uniform of funnel-shaped trousers and a high-necked jacket fastened with a belt, Itten was the most cultish of the Bauhaus masters. He was a devout follower of Mazdaznan, a neo-Zoroastrian movement that prescribed a strict vegetarian diet and breathing exercises, which he conducted at the beginning of each class. His methods attracted as many critics as disciples: he “had something demonic about him”, said one former pupil, which might not have been far off the mark. Among his many rambling essays was a text on how the white race represented the highest level of civilisation (this unsavoury side is glossed over in the museum).

The work students produced during these early years was as peculiar as the teaching staff. The winning design for the Bauhaus emblem, by Karl Peter Röhl, looks like a masonic seal, depicting a matchstick man holding up a striped pyramid surrounded by stars, circles and a reverse swastika. Plans for a Bauhaus commune by Walter Determann show a huddle of traditional log cabins in a forest setting, while another of his psychedelic drawings imagines housing and studios arranged in a crystalline starburst. It is a fusion of the folksy and expressionist that also imbues the woodcuts of the printing department, and the rustic pots produced under Gerhard Marcks, who moved the school’s ceramics studio to the town of Dornburg, where he lived with his apprentices like primitive settlers, making jam jars to sell at farmers’ markets.

It is all as far from the minimal “Bauhaus style” as could be imagined. The exhibition paints a picture of the school as a lively, ad hoc place with no single clear direction but a multitude of experimental goings-on, a heady melting pot of visionaries and vegans, conservationists and cosmologists. It was a messy, conflicted place, housing the competing interests of art for self-fulfilment and hard-nosed design for industrial production – and many shades in between. As Gropius put it: “My sole aim is to leave everything in suspension, in flux, in order to prevent our community from solidifying into a conventional academy.”

The Mies van der Rohe area of Bauhaus Museum’s new exhibition. Photograph: Andrew Alberts/Heike Hanada Laboratory of Art and Architecture

On the second floor, the wild world of Bauhaus theatre, music and parties takes over, with a section devoted to the school’s theatrical laboratory, headed up by Oskar Schlemmer. The experimental tutor – who made his name with the futuristic Triadic Ballet in 1922, with performers dressed as space-age lollipops – encouraged his students to work in miniature, developing marionette theatre and puppet shows. Many of their surreal creations are on show here, along with scenes from the outlandish dressing-up parties. “Tell me how you party,” Schlemmer proclaimed, “and I’ll tell you who you are.”

The more familiar, later side of the Bauhaus is not forgotten either, with a large area devoted to the products of the furniture and metalwork departments, from a pleasingly DIY-store display of doorhandles to shelves piled high with kitchen utensils, crockery and coffeemakers – stripped-back designs that have become so familiar.

But there are some gaping holes, which the centenary could have provided a timely point to address. Along with some Bauhauslers’ questionable attitudes to race, the subject of gender inequality is mostly ignored. As early as 1920, Gropius suggested that student “selection should be more rigorous … particularly in the case of the female sex, already overrepresented in terms of numbers”. He had reckoned on “50 ladies and 100 gentlemen”, but the reality was more like half of each, since the Weimar constitution guaranteed women unrestricted freedom to study. Some histories have painted a picture of merry equality at the Bauhaus, but this masks the reality that Gropius recommended women be sent straight from the Vorkurs to the weaving workshop, and he agreed with Marcks to admit “no women at all if possible into the [pottery] workshop, both for their sakes and for the sake of the workshop.”

Women’s work? … a 1923 building game by Alma Siedhoff-￼￼￼￼￼￼￼￼￼￼Buscher. Photograph: Klassik Stiftung Weimar, Bestand Museen

One of the few who asserted herself against these restrictions was Marianne Brandt, whose elegant metal teapots and ashtrays, composed from elementary forms of spheres and triangles, have become notable symbols of the Weimar Bauhaus. Her products are on show here in a glass vitrine (and on sale in the gift shop, from €150), but without so much as a caption. Similarly, the contribution of Lily Reich to the well-known works of Mies van der Rohe is barely mentioned.

The Himmelsleiter, or Stairway to Heaven. Photograph: Andrew Alberts/Heike Hanada Laboratory of Art and Architecture

As you leave the museum, down an imposing five-storey staircase in a narrow slot at the rear of the building, a large window frames a view of the rolling countryside, where a memorial tower stands in the distance. It marks Buchenwald, whose gates were designed by prisoner Franz Ehrlich, a former Bauhaus student. It is a powerful ending. As Germany faces the rising spectre of rightwing nationalism once more, the museum provides a poignant reminder of how fragile our freedoms remain.