“I LOVE the idea of shape-shifting and creating an identity for yourself, then creating another one, and then another. That’s what we humans really are: we’re shape-shifters. For some reason we’re continually trying to repress that. But we are shape-shifters."

So said model, singer, TV star and drag icon RuPaul in 2014, speaking no doubt from deep within the confines of a frock of exquisite fabulousness.

His words give a good enough explanation of what drives him and the many other drag queens who feature in cult reality talent show RuPaul's Drag Race, which recently finished a seventh series in the US and airs on Netflix in the UK. But they also give a clue as to why fashion and music are so often bewitched by drag culture. After all, what else is fashion about if it isn't creating identities?

Madonna's 1990 hit Vogue drew most obviously on drag culture. But in creating her Sasha Fierce alter-ego, Beyonce co-opted an adjective used frequently on the drag circuit and used that alter-ego to deliver the sort of songs you might hear drag queens belting out today: Single Ladies, Sweet Dreams and, of course, Diva. Lady Gaga soon followed suit (or rather frock) with a restless, gender-bending pop-drag hybrid, and colourful Trinidadian pop star Nicki Minaj is another who has borrowed from drag's over-the-top styling and gender-blurring schtick. Among her musical alter-egos is a "twin brother", Roman. Unsurprisingly, all three acts have a strong fanbase in the LGBT community.

The spell drag casts on fashion is particularly strong at the moment. As a result even Cher, the draggiest of female pop stars, is having what Planet Fashion calls "a moment". Now in her late 60s, she has found favour as both muse and model for designer Marc Jacobs.

Inspired by the famous outfit she wore to the 1986 Oscars – a shimmering, barely-there confection in black and glitter complete with a massive, spiked, Moulin Rouge-style head-dress – he sent models down the catwalk last year in feathered headgear designed by milliner Stephen Jones when he showed his designs for Louis Vuitton's Spring-Summer 2015 range.

Now Jacobs has gone one step further and signed Cher up as the face of his Autumn-Winter 2015 campaign. Accordingly, she's also the cover star on the new edition of Love Magazine. A bi-annual fashion publication edited by uber-stylist Katie Grand, it has a reputation for being both influential and envelope-pushing. So if Love Magazine says gay icon Cher is A Thing, then Cher is A Thing.

Pulling back and examining the zeitgeist, it's clear that LGBT issues generally have come much more into mainstream conciousness over the past few years, allowing representatives of those various communities to become more visible and their own icons and trailblazers to be re-assessed and celebrated.

The debate around gay marriage and America's subsequent legalisation of it are one reason for this, but there are others, such as Drag Race itself, Tom Hooper's upcoming film The Danish Girl and hit TV series Transparent. A comedy drama about a retired, married father of three who opens up to his family about wanting to be a woman, Transparent won two Golden Globes in January and has a whopping 11 nominations in next month's Emmy Awards. The Danish Girl, meanwhile, stars Oscar-winner Eddie Redmayne as 1920s artist Einar Wegener, who lived as a woman and became the first person to undergo gender re-assignment surgery in 1930. Early pictures of Redmayne in drag make him look extraordinary – or, as one arch commentator noted, like actress Jessica Chastain.

Frivolous it may seem and "fabulous" it may be, but in its celebration of "shape-shifting" and identity, and its willingness to battle repression, drag culture is clearly a movement that has balls as well as blusher.