Art Turning Left: How Values Changed Making 1789-2013 – review

Marat has just been stabbed through the heart. The revolutionary leader lies dead in his bath, one hand stubbing the nib of his once-powerful pen on the floor, the other still holding a false letter of introduction from his killer Charlotte Corday. The simple wooden crate he was using as a desk only moments ago has become a monument to his heroism: strewn with his writings and inscribed with the artist's own homage – "To Marat, signed David".

The Death of Marat by Jacques-Louis David is exhibit A of revolutionary art. It was a martyr's memorial, carried through the streets of Paris. It was a news report as much as a history painting, a protest but also a glorification, in which fully half of the canvas holds nothing but a kind of beatific twilight, turning the pale corpse into a secular pietà. A work of astounding originality, the picture is one of the undisputed masterpieces of European art – but that is not how they want you to see it at Tate Liverpool.

David's painting is nailed up like one more item on an overcrowded noticeboard, opposite a wall plastered with newspapers and next to not one but four identical prints based upon Marat's head. For what concerns the curators is not the painting itself but the fact that David put his art to the service of the Republican cause, allowing a print-maker to convert the picture into a crude mass-reproduction image.

The subject of this thorny, chaotic, ill-selected, badly presented but undeniably interesting show was never going to be art itself. Its theme is the influence of leftwing politics on the production and reception of art. The focus is on co-ops, collectives, anarchists and situationists, on underground art, anonymous art, free art and community movements. It is heavy on slogans, documents and posters. It is all about Art for All.

Every work is here to raise an issue, present a theory or propose an argument (in many cases the work is the argument, spelled out in capital letters). Every work is treated as an example.

So the show has art made by many hands – big political allegories painted by Tim Rollins and his teenage Kids of Survival; and it has art that is pointedly anonymous – prints and paintings signed by nobody so that their value cannot be boosted by an artist's reputation.

Banner, 2005 by Ed Hall, for Alan Kane and Jeremy Deller’s Folk Archive. Photograph: © the artists, courtesy the British Council Collection

It has work made by whole communities – large tranches of British folk art from the archive compiled by Alan Kane and Jeremy Deller. And it has work that anyone can make here and now in the gallery, stamping subversive epigrams on bits of paper – I particularly liked "Looking Without Paying Is Thievery" – or embroidering pictures on a golden cloth.

There are swatches of William Morris wallpaper to put you in mind of anti-industrialism, the arts and crafts movement and the Socialist League, and constructivist dress designs by the Rodchenko family workshop. The show pays obligatory homage to the Bauhaus, and the notion of absolute equality between photographs and fabric, ashtrays and paintings. And it has Walter Crane's banners for the Holloway branch of the Workers' Union, battered but still expressively defiant.

And slap in the middle is an office where people can go to debate the usefulness of all this art – art, of course, supposedly having no uses.

This is emblematic of the whole project: it is all about arguments, not images.

Can art affect everyone, does it matter whether we know the artist's name, does equality change how art is made? Art Turning Left covers the subjects, ticks off the artists, ploughs diligently through its themes. Sometimes it comes up with a work of real power, but generally it is that most dismaying of art experiences: a doctoral thesis in the guise of an exhibition.

So it asks whether art can infiltrate society, for instance – a perfectly good if archaic question. But it's naive to offer up the great textile designs of Lyubov Popova as an affirmative instance, as if the Russian avant garde had not been atrociously manipulated and abused by the Soviet regimes.

And it asks whether art can find alternative distribution systems outside the market and gallery circuit, and then presents a wall of almost parodically obscure artist-run newspapers as if this was any kind of answer.

How can artists buck the capitalist system? They can sell their paintings by the metre, post their works in the form of chain letters, make art that cannot be bought because it melts, burns, explodes or never existed as a tangible object in the first place. The questions that shape each section feel, at times, like a pub quiz for art history students.

But the show never engages with the fact that a voracious market exists for this supposedly unbuyable work. André Cadere's striped sticks, the pilgrim staffs with which he walked the world, are bought and sold. The masticated remains of John Latham's famous protest – chewing up a copy of Clement Greenberg's Art and Culture in 1966 – were eagerly purchased by the Museum of Modern Art in New York.

An air of freedom, it is true, runs through some of the art from the 1960s and 70s. It's good to see the Guerrilla Girls' radical slogans once more – "Thou shalt not be a Museum Trustee and also the Chief Stockholder of a Major Auction House" – if chilling to think how pertinent they remain. And anyone who wasn't around at the time may relish the festive spirit of the King Mob collective, whose members tried to give away all the Christmas toys in Selfridges to small children in 1968, and were rapidly arrested.

The fact that most of the artists in this show were vehemently in favour of free distribution and art for all, incidentally, is a paradox that will not be lost on anyone who has paid the £8.50 ticket price.

The deeper you go into the show, the greater the divergence between ideas and images. It may be fascinating to learn of the king of Sweden's alchemist, a secret anarchist who aimed to flood the market with so much gold that money would eventually become worthless, but the accompanying sculpture (a replica of his machine) isn't interesting at all.

And much as one might admire the collectivist principles of the neo-impressionist Maximilien Luce, the painting of steelworkers at the furnace, while indicating his political sympathies, is hardly his most electrifying work.

There are exceptions, particularly the superb black-and-white woodcuts of the German artist Georg Arndt, condensed visions of Europe in the 1930s that deploy irreducibly simple graphic forms – bowler hat, bunting, feather, boot, fist – with extraordinary flair and subtlety to warn of the coming disaster. They are a revelation, great art as a form of public address, and they raise the whole tenor of the exhibition.

Arndt believed in a universal language, in the common good of art. By the end of this show, a certain nostalgia sets in for a time – and an art – of such idealism. Of course that dream is still alive (there are many instances in the excellent supplement published by Tate Liverpool) but so is its exact obverse, an art world symbolised by the grotesque gorging upon investments that is the annual shopping trip of the Frieze art fair.