Friday night in Edinburgh and a troupe of transgender Thai showgirls and their kilted male friends – plus Jamie John, a self-described gay dwarf – are onstage in highland regalia swaying to The Bonnie Banks o’ Loch Lomond, the words of which are being enthusiastically bellowed by the audience. Part wedding reception, part concert, part cabaret, but with a potent flavour all of its own, this Saltire-flying extravaganza is the climax of the latest show by The Lady Boys of Bangkok, who made their debut in Edinburgh 21 years ago, and have been coming back every year since.

While critics and much of the media have more or less ignored the Lady Boys, they’re the biggest show on the fringe, drawing in a cross-section of local Scots. There are grans, family groups, hen parties and young couples tucking into wine and Thai food at tables in a sweltering big top; tourists and London hipsters however, are conspicuous by their absence. “It’s one of the things of the fringe, you’ve got to come and see it,” says audience member Gary Erskine during the interval. Will he be going to see much other stuff? “This is pretty much it.”

So – at £22.50 a ticket (and a tenner more in the “platinum seats” near the front) – what keeps drawing in the fans? First, there’s the glamour: 14 showgirls, the titular Lady Boys, who lip-sync to a variety of pop bangers dressed as famous divas – Kylie, Rihanna, J Lo, Whitney. “It takes femininity to a different level,” reckons Angela Buchen, one of many fascinated female punters (on some nights, the crowd is 80% women). “It’s a bit bewildering, that they’re men underneath. It’s actually phenomenal, trying to get your head around it.”

Behind the scenes … the Lady Boys of Bangkok minutes before curtain up. Photograph: Murdo MacLeod/The Guardian

The lady boys’ tucks – the ability to make the penis and testicles seemingly disappear when wearing tight bikini bottoms – are a particular wonder. “It’s the tricks of the trade, that’s all I can say,” says John, who shares a dressing room with them. “Seeing is believing!”

Then, making this an 18-certificate show, there’s the sleaze. In scenes that call Alan Partridge’s sexual fantasies irresistibly to mind, there are three interludes in which straight Scottish lads are dragged, not entirely unwillingly, on to the stage and felt up by Decha Nuchangsing, a sturdy lady boy with a lecherous demeanour. “They’re tied to a chair and he gives them rather an exotic lap dance, which nine times out of 10 the men enjoy,” says John. Wearing a sequinned jacket, John also presides over a lewd Countdown parody in which the word “happiness” becomes … well, it doesn’t take Carol Vorderman to work it out.

The Lady Boys’ main appeal, however, is a communal one. As a raunchy version of One Night in Bangkok set in a hostess bar (this is not a show that shies away from its roots in the Thai sex industry) turns into a Queen tribute in which the cis male dancer Arthur Dy Saensuk dons a moustache to perform as Freddie Mercury, the audience rises to its feet to sing along to Don’t Stop Me Now. Then there’s a shameless selection of crowd-pleasers including Sweet Caroline, This Is Me, YMCA and I’m Gonna Be (500 Miles) by the Proclaimers. Staying in your seat is impossible; as I try to take notes a woman behind me grabs my arms and waves them around as the Lady Boys get stuck into Whigfield’s Saturday Night.

‘Seeing is believing’ … behind the scenes with the Lady Boys of Bangkok. Photograph: Murdo MacLeod/The Guardian

With its unashamed embrace of cheesy euphoria, it’s not hard to see why The Lady Boys of Bangkok will never be cool – and why they also manage to reach an audience not catered to by much of the fringe. Yet with a plethora of trans and non-binary performers finding their voices in Edinburgh, do the silent, miming Lady Boys seem like relics from another era? While the show has an LGBT cast, it was created and directed by the straight circus impresario Phillip Gandey, and is aimed squarely at a mainstream, heterosexual audience (“This is not a gay show,” the Lady Boys’ spokesman Tony Wilkie-Millar tells me firmly).

It’s hard to deny that the Lady Boys are being somewhat exoticised. Audience member Davey Nicoll has travelled to Edinburgh from Inverness to watch the act. “Everybody knows what it is, but you come and enjoy it all the same,” he says. So what is it? “It’s chicks wi’ dicks! It’s curiosity, it’s like PT Barnum, you know The Greatest Showman? It harks back to that for me.”

Gandey says that, while prurience may get some people through the door, it’s the quality of the performance that counts. “When we first put it on, curiosity was the only selling point, and that’s still there, but that lasts 10 minutes. If it wasn’t for the standard that these people perform at, the show wouldn’t still be going. One of my most proud achievements is what the Lady Boys of Bangkok has done for transgender people in the United Kingdom. They were the butt of a joke 21 years ago and we’ve made it mainstream. We did This Morning several years ago with Richard and Judy and when they introduced them on the show it wasn’t ‘This is a show about men trying to be women’ they said ‘We’re welcoming one of the UK’s most fabulous dance troupes.’”

‘Not entirely unwilling’ … audience members join the troupe on stage. Photograph: Andrew Payne

The day after the show, I sit down with two of the Lady Boys: Sonia and Bombay. In Thailand, lady boys are called kathoeys, and are regarded as a third sex. Sonia and Bombay don’t have much English, but it’s pretty clear from what they say that to be transgender in Thailand is to face discrimination and prejudice. Showbusiness is one of the few arenas in which they can be celebrated for who they are.

Theoretically off-duty in dangly earrings, lipgloss and prom dresses, Sonia and Bombay still project megawatt glamour. This is how they dress all the time. Showgirls to their immaculately manicured fingernails, the pair look bored stiff when I try to engage them in gender politics, but come alive when I ask what divas they enjoy embodying. “Of course, Kylie,” says Bombay, who does a sensational re-enactment of the video to Can’t Get You Out of My Head. “She is the most popular woman in the UK.”

In the programme, Sonia and Bombay are listed as “Mr Uten Pengsa-ard” and “Mr Kornwarin Kaewjaima”, which seems like a deeply retrograde act of misgendering. Nonetheless, the illusion – if it’s even appropriate to call it that – of changing gender is central to their act. Wilkie-Millar says that if any of the Lady Boys transitioned fully, they would no longer be suitable for the show, the same argument that got RuPaul criticised for lack of inclusivity when he told the Guardian that trans women shouldn’t compete on RuPaul’s Drag Race.

In this way, there’s a lot about the Lady Boys of Bangkok that sits uneasily at Edinburgh in 2019, which aims to be as trans-inclusive as possible: cast lists come furnished with preferred pronouns, urinals are covered up in order to make toilets gender neutral. Nonetheless, Jonny Woo – who has been at the vanguard of the current boom in queer performance, both as a drag queen and co-owner of London venue the Glory – sticks up for the troupe. “The Lady Boys of Bangkok are coming from Bangkok, not Dalston, and I don’t think we should put our current moral compass on a company that’s coming from [a different place],” he says. “If they choose to entertain straight audiences, it’s up to them. Queer is in, the trans conversation’s happening, but there’s not just one voice – there’s space for it all.”

Intimate moment … getting ready backstage. Photograph: Murdo MacLeod/The Guardian

What about the straight audience’s preoccupation with their genitals? “I don’t think that’s much different from watching RuPaul’s Drag Race,” Woo says. “The transformation of a male identity into a female identity still fascinates and entertains, so to say, ‘It’s old school, it’s not where we’re at now’ – there’s tons of drag in Edinburgh now, but although we might add some politics to it, we’re still playing with the transformation.”

Rather than politics, what the Lady Boys want to provide, says Wilkie-Thomas, is escapism. “We’re trying to celebrate being alive and having fun. A woman in the audience told me she’d had chronic back pain for the last six months and this was the first time she’d not felt it. We’re not trying to get our audiences coming out and saying, ‘I’m all for gender freedom.’ We want them to come out and say they’ve had the best fun they’ve had for months.”

Maybe there is something inherently subversive or political in what the Lady Boys do in any case. Edinburgh council certainly keeps them at arm’s length. Despite their blockbuster popularity, they’ve been turfed out of the Meadows, where they’ve performed for the last 16 summers – “which is why the fringe’s top-selling show now finds itself on a derelict brewery site outside the city centre,” says Gandey.

“We just want to be happy on the stage and express the real us and we hope that the audience accept us as who we are,” says Saensuk. But by the end of the show, the feeling in the room is of more than just acceptance. Maybe it’s the delirious effect of watching 500 Miles performed by Lady Boys in sporrans, but as a sign descends from the ceiling declaring “The Lady Boys of Bangkok love Scotland”, it’s clear that Scotland unreservedly loves them back – a feeling that seems intense enough to last another 21 years.