It happened, as most of the best fashion moments do these days, at Cannes. I’m not talking about Demi Moore wearing a pink bow the size of a dog, or Jane Fonda sparkling in Gucci to the point of blindness, but John Travolta, of all people, who appeared at the festival this week to debut a new film and a new look, the centrepiece of which was a beret.

He actually had three in rotation, in black, brown and cream. On the seafront boulevard La Croisette, he paired them with wire-frame spectacles and a beard that appeared to have been applied with a felt-tip pen. A beret, beard and specs you say? Hardly a radical glow up for a 72-year-old celebrity. But that didn’t stop images of Travolta from going viral, sparking some lively online conversations comparing him to – in no order – a barista, a Bond villain and a character from Guess Who?.

Happily, the man himself was delighted to reveal his inspiration in a charming interview with CNN. Since he was marking his first foray into directing, Travolta had decided to dress like film directors from the past. “You’re an actor,” he had told himself, scrolling through images of Ingmar Bergman and Roberto Rossellini in similar getup. “Play the part of a director.” In other words: manifest.

Travolta’s admission had a spectacular effect in softening the hot takes. He had simply dressed for the part he wanted, or at least wanted to be known for. And however absurd his outfits were – particularly when he was waving his honorary Palme d’OR around – there was a small part of me, and perhaps all of us, that felt incredibly seen.

Who among us has not used clothes to try to shift an outcome? Perhaps as a way of signalling an attempted career change, or to forge a new identity after a breakup. Or in my case, to partly defang the industry I work in – fashion – by wearing Birkenstocks (though it helps that they’re comfy too). However you feel about clothes, the way we dress affects how we feel. And the way we dress also affects how other people feel. This is not cosplay. It’s enclothed cognition. The only mistake Travolta made was committing too keenly to the bit.

It’s worth adding that red carpets are fundamentally weird places. Too much attention must be hell for celebrities, but its absence is a lot worse. However instructive the dress code, however famous its participants, when the primary focus is on the films rather than the clothes, as is the case at Cannes, stars can go for broke. But it’s trickier for directors, who are toggling between necessary publicity and a desire to be taken seriously as auteurs.

Add to that just how cruel, fickle and frankly ageist Hollywood can be, even to men, and particularly when it comes to reinvention. Who can blame Travolta for buying some new hats to try to shift the invisible lever of relevance, even if said hats make him look more like a mime? Is it any different to Taylor Swift wearing Elizabeth Taylor’s jewellery this week in the hope that some of the latter’s star power might rub off, or Pep Guardiola wearing plaid shirts as a way of quiet quitting from his job at Manchester City, or even Kim Kardashian wearing Marilyn Monroe’s 1962 “naked” dress to the Met Gala in 2022 not to pay homage to its original wearer, but rather as a way of inviting comparison?

But it’s in politics where this sort of method dressing occurs most intently, where clothes serve as an exercise in would-be-leadership theatre and ultimately signal the kind of politician you want to be.

Right now, Andy Burnham is dressing for the job he wants, which is Keir Starmer’s. To show that he’s a man of the people, he is out in retro Everton shirts and running shorts – the go-to soft launch garment of choice (I’ve got stamina!) – or bomber jackets and tees, deliberately anti-Whitehall dress codes at odds with his beleaguered rival. Then there’s Wes Streeting, who has long been a wearer of the centrist blue suit – and a carrier of its implicit ideology. He is, as he always has been, dressing for the big job, while taking a leaf out of the Barack Obama playbook of easy-breezy leadership by occasionally ditching his tie. Or Angela Rayner, who as demonstrated in her recent sit-down interview with ITV, is simply wearing more red.

The problem is, dressing the part can only take you so far. You can dress for the job you want but it doesn’t mean you’re any good at it. Go too hard and you risk veering into parody or even Halloween. Still, at least Travolta earned the right, having actually directed a film (albeit a middling one). As for the others? There’s only so far a pair of shorts can manipulate public perception.

• Morwenna Ferrier is the Guardian’s fashion and lifestyle editor