‘That belongs in a museum.” “So do you!” Indiana Jones (youthful, anti-establishment, recent thief of priceless treasure) is the first speaker; Panama Hat (fusty remnant of colonial Britain) the second. The scene is famous. But it also strikes the modern viewer as rather out of date: those fighting over what belongs in a museum now split, politically and demographically, in precisely the opposite direction.

Western museums still tend to think of themselves as culturally open, their purpose to celebrate diversity and international understanding. But in recent years young progressives have been turning against them, arguing that a number of their displayed items – particularly looted ones – should be returned to their countries of origin. The rightwing establishment, meanwhile, generally believes these objects should stay put.

This – particularly cultural – culture war reignited towards the end of August after a spate of thefts at the British Museum. Some 2,000 objects had reportedly been stolen over several years, leading to the sacking of a curator, the resignation of director Hartwig Fischer and renewed calls from countries such as Nigeria, Greece and China for contested artefacts to be returned. After all, they say, the British Museum can no longer claim to be a safe repository for their treasures, one of its longest arguments for keeping them.

The British Museum lags behind other institutions when it comes to restitution. It has not, for example, returned its Benin bronzes, Nigerian sculptures looted at the end of the 19th century in a savage attack by British troops, and the centre of a long tug of war between the respective governments. Even so, its critics might be applying pressure in slightly the wrong place. The museum is constrained by the British Museum Act of 1963, which prevents it from permanently returning most objects (long loans are allowed). It is ultimately up to parliament to change the law.

This will be tricky to manage. The current Tory government is unlikely to want to get on the “wrong” side of a culture war, and a Labour one may want to keep out of it altogether. Even so, if the museum’s director and trustees were to lobby the government to change the law and allow them to return items, it just might work. And the law should change. Only one side of this war is backed by the facts: the arguments against restitution, one by one, are crumbling into dust.

The idea, first, that western museums are the safest place to store the world’s treasures has received a blow in recent weeks but has also been disproved many times over. Museums have been attacked – during the Second World War, Liverpool Museum’s Benin bronzes fell victim to bombs – swathes of objects have been sold off to private collectors, and others, of course, have been stolen. The British Museum’s security, to say the least, has holes. (A reporter posing as a work experience trainee once walked out with the foot of a statue worth £20,000).

A second argument, that returning some pieces would eventually leave museums with lonely plinths in echoing halls, looks increasingly ridiculous. Museums are swimming in vaults of booty they can hardly hope to catalogue, let alone display. After 40 years of work, only about half of the British Museum’s swag, its website admits, have been added to its main database. The museum is a species of iceberg, with only a fraction of its glittering bulk above the surface. Items can go missing for years without anyone noticing.

The oft-repeated argument that these objects are more accessible in busy western hubs doesn’t stand up either. Why shouldn’t Nigeria’s cultural history be accessible in Nigeria – as well as the extra tourists this might encourage?

And returning the objects doesn’t necessarily mean losing them altogether. “A lot of the key people on the Nigerian side of the argument want some of the bronzes to be in London,” says Barnaby Phillips, author of Loot: Britain and the Benin Bronzes. “They want ultimate ownership to be theirs, but they also want their culture to be displayed around the world – so they would be the ones sending them out on loans.”

And there’s a further, more existential, problem for museums that display looted goods. How to reconcile it with mission statements about promoting understanding between cultures? Ironies cannot help but abound.

Previous directors of the British Museum have variously tried to argue against returning the Benin bronzes on the basis that the “quest for truth” facilitated by their collections will eventually lead to “hierarchies” being “subverted” as well as “greater tolerance of others and of difference itself”. In other words, that keeping the swag from our brutal history of conquest will eventually stop such incidents happening in the first place.

The plaque next to the Benin bronzes was updated during the pandemic: it is now admirably frank. But the museum’s Easter Island statue, which the island wants back as it “embodies the spirit of an ancestor”, sits in a gallery that claims to “investigate people’s reliance on relationships – with… ancestors, and the land and sea – to maintain wellbeing”. They’ve investigated it, have they? Well, that’s one word for it.

A central problem here is that these objects are not just a record of colonial oppression and historic crimes but, to many, the thing itself perpetuated. This compromises a museum’s role as educator: it must tiptoe round the subject, talking of “uncomfortable histories” that still need to be “explored”.

In fact, there are only two ways, I think, for the British Museum to avoid these vast hypocrisies. One: update their mission statement to something like this: “The history of our species is one of brutal exploitation and the joy of displaying the spoils. Despite our modern affectations, we are at base no different. Come revel in the war booty this nation has accumulated.”

Or they could lobby to change the law, so that looted and stolen items can be returned. Their choice.

• Martha Gil