He drew portraits for Italian dukes, sketched for the papacy and died at the court of a French king. If there is any artist who defies nationhood it is surely Leonardo da Vinci. Yet last week, Leonardo’s cosmopolitan legacy was caught up in an extraordinary intergovernmental spat when Rome renewed its threat to block Italian galleries from lending to the forthcoming Louvre exhibition commemorating the 500th anniversary of Leonardo’s death.

Leonardo was Italian, after all. Why don’t they loan us the Mona Lisa? Lucia Borgonzoni

This fine-art impasse has been brewing since November when the new Italian culture minister, Lucia Borgonzoni, from the far-right League party, described a previous government’s decision to lend to France as “one of the biggest, most shameful acts with regard to cultural heritage”. Bottom line: there could be no question of a loan without La Gioconda coming the other way. “Leonardo was Italian, after all. Why don’t they loan us the Mona Lisa?”

The row exposes, in populist colour, the terrible danger for creative exchange when politicians claim possession of artists as national icons. More than that, what the Louvre-Leonardo dispute reinforces is the urgent need for museums to stand up to today’s encircling clamour of chauvinism and cultural essentialism.

There is a long and beautiful history of princes marshalling art and design for propaganda purposes. We would not have nearly as glorious a memory of Henry VIII and his wives without the brushwork of Hans Holbein (a Bavarian). And what better insight into the Habsburg court of Philip IV of Spain is there than Diego Velázquez’s baroque cycle of royal portraits?

Over the past three centuries, nations have proved just as adept as dynasties in ensuring that culture serves a wider ideological agenda. When Britishness was forged during the latter half of the 18th century on a diet of anti-Catholicism, empire and war, it was William Hogarth who best codified this developing sense of identity. His O the Roast Beef of Old England (“The Gate of Calais”), with its garish depictions of fat monks, bare-footed nuns and effeminate French soldiers, was a single-sheeted declaration of the glory of Great Britain.

On the other side of the Atlantic, Thomas Cole (a British immigrant) and the Hudson River School of landscape artists would do the same for the US. Their vast, arching canvases depicted America as a new Eden, liberated from the corruption and filth of old Europe. It was the artistry of manifest destiny that helped to mould an emergent US sensibility.

History abounds with moments of diplomatic tension relieved by artistic partnership

Today, the process is no less overt, with art and monumental architecture heavily involved in national self-assertion. On the West Bund of Shanghai, for example, there is an incredible cluster of swish galleries and museums marking modern China’s new confidence when it comes to cultural patronage. And this March, unbowed by sanctions, Doha will open its stunning Jean Nouvel-designed National Museum of Qatar, filled with some of the greatest Islamic art in the world.

But none of this nationalist lineage applies to Leonardo. Together with Erasmus of Rotterdam, Leonardo was one of the leading lights of Renaissance humanism. He was part of an influential school of quattrocento artists, writers and philosophers who moved seamlessly across the secular and spiritual, artistic and scientific, political and state boundaries, jettisoning the scholastic “middle ages” to champion the creative capacity of man. His Vitruvian Man (c 1490), with its anatomical depiction of human proportions rooted in classical purity, is a testament to the shared essence of humanity.

From Florence to Milan to the Loire Valley, Leonardo was a child of the Renaissance for whom modern claims of nationhood make no sense. Clearly something else is going on with this cultural blockade. On the one hand, there is Leonardo lunacy. As the controversy over the purchase, authenticity and now whereabouts of the $450m Salvator Mundi has revealed, this genius artist-engineer of 500 years ago has the ability to send auction houses, scholars and even nations half-mad. Then there is the open rancour that exists between France’s progressive, pro-European President Emmanuel Macron and Rome’s more nationalistic Five Star-League coalition, with its official backing of the gilets jaunes insurgency.

President Kennedy and his wife go to see the Bolshoi in Washington in 1962. Photograph: Everett Collection Historical/Alamy Stock Photo/Alamy Stock Photo

Yet the dispute highlights a wider, worrying trend for populist governments to seek to inhibit artistic exchange. A programme of economic nationalism, paranoid chauvinism and anti-immigration can quickly seep into the cultural sphere. In 2017, President Nicolás Maduro banned Gustavo Dudamel and his lauded Venezuela national youth orchestra from touring America after the conductor condemned the killing of musicians in Caracas. “Welcome to politics,” sneered Maduro. In turn, US sanctions on Tehran have heavily affected the ability of US institutions to collaborate with Iranian artists and curators. Most absurdly (if tellingly), in Russia, local authorities have sought to prevent Kaliningrad airport being renamed in honour of its most celebrated son, Immanuel Kant, precisely because of the 18th-century philosopher’s Enlightenment cosmopolitanism.

By contrast, history also abounds with moments of diplomatic tension relieved by artistic partnership. At the height of the cold war, in the aftermath of the Cuban missile crisis of 1962, the Bolshoi Ballet performed to rapturous audiences across Washington. From lending the Parthenon sculptures to Russia to hosting China’s terracotta army in Liverpool, British museums and galleries have long appreciated the importance of cultural engagement outside the diplomatic strictures of government. Today, Daniel Barenboim’s West-Eastern Divan Orchestra, with its array of young musicians drawn from across the Middle East, is arguably the most inspiring example of art speaking with one language.

With the liberal sky darkening from Hungary to Brazil, it is the responsibility of galleries, orchestras and theatres to defend these principles of enlightenment, cosmopolitanism and knowledge. As social media memes spread false news, and political divides become more embittered, our role as trusted institutions to contextualise current controversies fulfils a vital civic function. For we have the collections, born of thousands of years of empire, trade and migration, that dispel those alluring myths of national purity and, instead, tell the real, heterogeneous story of human creativity. Surely, that ethos of exchange and inquiry is the true humanist inheritance of Leonardo – and not this demeaning tussle as to whether Paris or Rome really own his genius.

• Tristram Hunt is director of the Victoria and Albert Museum