Gender-bending and LGBTQ-oriented pop music becoming popular predates the 1980s. The most obvious manifestation of this was the androgyny of the glam rock genre associated with T.Rex and David Bowie and Roxy Music, et al, which had its biggest successes in the early 1970s. In terms of LGBTQ music, the glam genre had an openly gay musician in Jobriath (who can be seen performing here), who never became a big star, but who later musicians found inspirational (Okkervil River have a song called 'Bruce Wayne Campbell Interviewed On The Roof Of The Chelsea Hotel, 1979'; Bruce Wayne Campbell being Jobriath's birthname). The glam rock movement of the 1970s was gender-bending in the sense that you got long-haired men wearing makeup and frilly clothes, and who liked to claim a flirtation with bisexuality (though none apart from Jobriath were openly gay at the time). The Australian hard rock band AC/DC were originally positioned as a glam rock band in the early 1970s; AC/DC was polari slang for bisexuality, and there's early footage of AC/DC performing on the Australian TV show Countdown with lead singer Bon Scott dressed up like a schoolgirl, in make up. Given AC/DC's later reputation as a man's man's hard rock band, the cover of their 1975 album High Voltage for the UK market is kind of hilarious - they're very clearly being positioned as a glam rock band here.

As to why the 1970s glam rock movement was successful, it's generally thought that glam rock appealed to pre-teens and teens who simply enjoyed the theatrical nature of the performances. The brightly coloured outfits worn by glam rock groups were particularly noticeable on the (relatively new) colour televisions of the era as the young people watched shows like Top Of The Pops in the UK and Countdown in Australia (glam rock was never as successful in America as it was in the UK and Australia, and American glam metal bands of the 1980s sometimes made good business covering UK glam rock from a decade ago, e.g., Quiet Riot covering Slade's 'Cum On Feel The Noize'). However, there was a certain logic to glam rock's androgyny, given the public opprobrium that younger long-haired male hippies got from older generations, who considered their style and taste unmanly; why not just go the whole hog and reject those notions of masculinity?

Many of the glam rockers were also inspired by the late 1960s group the Velvet Underground, where songwriter Lou Reed often wrote about the people associated with Andy Warhol's Factory (which the band was famously associated with, with Warhol designing the cover of their first record). Lou Reed's most famous song 'Walk On The Wild Side', from 1972, at the height of the glam rock thing, has the verse about 'plucked her eyebrows on the way, shaved her legs and then he was a she', but several Velvet Underground songs reference LGBTQ/gender-bending behaviours and people ('Candy Says', track one on their 1968 self-titled album, is about the transgender Factory personality Candy Darling, and begins with the words 'Candy says I've come to hate my body / And all that it requires in this world'). Similarly, slightly predating the glam rock era was The Kinks' 'Lola', in which Ray Davies sings that 'Girls will be boys, and boys will be girls/ It's a mixed up, muddled up, shook up world/ Except for Lola'; of course, Davies also sings 'I know what I am and I'm glad I'm a man, And so is Lola.' Notably, for songs written at the end of the 1960s, there's little judgement or making fun in 'Candy Says' or 'Lola'.

There was also the LGBTQ-oriented nature of a lot of disco - an openly gay black man going by the name Sylvester had a hit in 1978 with 'You Make Me Feel (Mighty Real)', and who got called 'the Queen of Disco'; the LGBTQ nature of disco is discussed more in this old answer of mine, and some more in this answer of mine about the Village People's YMCA.

One thing to remember about rock music/pop music in the 1970s and 1980s, which is a little harder to understand now (simply because the music is now ubiquitous enough that conservative political figures try to identify with rock'n'roll) is that youth-oriented pop music was very often countercultural, meaning that it came from subcultures and scenes and communities that rejected some of the mores and strictures of mainstream society. There's not that much of a stretch from utopian hippie ideals of the 1960s about free love to an acceptance of homosexuality. And while a lot of the New Romantic pop of the 1980s - the likes of ABC, Culture Club, Duran Duran, Human League, etc...probably what you were thinking of when asking this question? - now seems very mainstream, it had a definite countercultural tint to it in the 1980s.

The 'theory' of the New Romantic movement has a lot to do with the NME journalist Paul Morley, who had a background in critical theory, and who brought that to his NME journalism. In the last issue of the NME in 1980, Morley christened the kind of music he was looking for as 'New Pop', music which was openly theatrical and mainstream-ambitious, and devoted to the momentary pleasure of pop as opposed to trying to make 'classic' music - but also music that had a hefty dose of punk ideology. The music that Paul Morley called New Pop was frequently influenced by David Bowie and Roxy Music in particular - music with an LGBTQ tint to it. Morley appeared in the video clip for ABC's 'Look of Love' and then went to manage and promote Frankie Goes To Hollywood, who were probably the most overtly LGBTQ group of the 1980s (and best known for 'Relax'). Morley played up the homosexual themes of 'Relax', doing a media blitz with slogans like 'ALL THE NICE BOYS LOVE SEA MEN', and making sure that the video was set in a fairly obvious homosexual milieu.Additionally, the New Pop movement happened to coincide with the advent of MTV, a music video channel at the time, which found that its audiences responded to videos that were colourful and theatrical and a little edgy, which corresponded well to the kind of thing the New Pop groups (to use Morley's term) were doing. The success of Frankie Goes To Hollywood was limited; once it became clearer to the initially-uncomprehending public how gay 'Relax' was, the group kind of tanked commercially; there was definitely a tension between the public's desire for music that had a certain upbeat theatricality and the still-rather-conservative public's rejection of those underlying values. Simon Reynolds in Rip It Up And Start Again: Postpunk 1978-1984 claims that the downfall of Morley's approach to Frankie Goes To Hollywood was its reliance on the shock tactics of Malcolm McLaren's management of the Sex Pistols for a band that fundamentally wasn't the Sex Pistols.

The comparative visibility of gay artists and of gender-bending themes in rock music is in many ways a continuation of musical traditions of the 60s and 70s -- bisexual counterculturalists like Janis Joplin and Lou Reed, David Bowie in a dress or in a bodysuit with Kabuki makeup and dyed hair, Jimi Hendrix teasingly singing the frequent mondegreen of "'scuse me while I kiss this guy", long-haired hippies and pierced punks. But in other ways the visibility of queer artists and queer images is due to developments in gay rights during this era -- Stonewall, developing gay liberation movements and activism overlapping with counterculture movements rather than the somewhat staid activism of the Mattachine Society and Daughters of Bilitis, heightened gay visibility, and pushback on homophobic public figures and campaigners like the conservative Christian and overtly homophobic Anita Bryant. But the 1980s were far from a stagnant time or a political plateau for the gay community after the events of the 1970s. Between AIDS activism, public responses to homophobic government policies, public responses to homophobic public figures and campaigners, broader homophobic social attitudes and the rights of queer youth, there was a lot to keep the LGBT community busy in the 80s and a lot of ground to be gained or at least fought for. The accomplishments of the gay community in the 1980s laid the groundwork for later developments like same-sex marriage, and to activists those accomplishments didn't seem decades away -- many of the same activists who agitated for the rights of people with AIDS in the 1980s were agitating for the legal rights of same-sex partners in the 1980s and 1990s.

Beginning with one type of gay-friendly musician, there are worse places to start than with Grace Jones. Grace Jones had become familiar with the gay nightclub scene in the 60s and 70s, in New York and Paris, and she found herself pretty popular in it. This was due to her musical sound and strong performances as well as due to her strikingly androgynous physical appearance. Grace Jones as a model looked otherworldly and impossibly glamorous, in a way that evoked both female masculinity and male femininity; Grace Jones as a performer was raunchy and powerful in a way that evoked drag and the gay discos she performed in as well as frequented. The disco of the 70s and early 80s was a nexus for gay performers and gay listeners, and it in some ways forged the association between electronic and pop music with gay and gender-nonconforming performers of the 80s. Some disco musicians were queer themselves, others embraced or rebuked their gay fanbases -- Donna Summer alienated a big swath of her fans with her 1983 religiously-motivated remarks to the effect that HIV was God's punishment for homosexuality and homosexuality itself was unnatural and ungodly. This had a chilling effect on her popularity not just within the initial crowd who'd heard her comments but within the broader gay community -- publications like Outweek were still discussing her remarks in 1989 when she made an equally religion-infused public apology to gay publications and activist groups. But the varied reaction of women musicians (not necessarily queer or not-queer themselves) to their gay male fanbases and status as "gay icons" could be material for a whole other post.

There certainly were queer/gender-nonconforming performers in other genres, whole offshoots of punk rock in the form of queercore arising in the mid-80s and folk musicians like Tracy Chapman in the late 80s, but when you think "why was 80s music so gay?" you're probably thinking of electronic music, pop, and new wave. Annie Lennox of Eurythmics was another androgynous female performer -- cropped hair, shoulderpads, leather! -- but the model of androgyny in electronic and pop music of the 80s was less about masculine women and more about male and female musicians and fans you couldn't necessarily tell apart at first glance.

Elton John as a performer had come out as bisexual in the 70s, but was on his way to coming out as gay in the later 80s. Pop and new wave groups with gay members or gender-bending aesthetics like Dead Or Alive and Boy George performing with Culture Club in 1983 elicited immediate comment as well as imitation. Lots and lots of imitation. They became successful due to their sound, but their look was the topic of discussion. Other groups who played more overtly with sexual themes in their music and videos ran afoul of censorship. Witness the 1984 dust-up over the lyrics to Frankie Goes To Hollywood's "Relax" and its accompanying music video -- in ad campaigns and album covers FGTH's record company played up the band's association with sexuality and with homosexuality in particular, but it was raunchy homosexuality rather than glamorous androgyny, allusions to big dicks and fisting and aspects of BDSM. This got the group plenty of attention, but it wasn't the road to pop-stardom or a recipe for becoming a household name. During this same time new wave bands with queer lyrical themes like the Pet Shop Boys arose, but frequently these performers held off on "coming out" in a press sense until the 1990s. Some of the popular association between the 80s and gay bands/gay music may be enhanced with the gift of hindsight, in the case of groups like Wham! where George Michael's homosexuality became sufficiently widely known later to tint recollections of both members of the group indelibly.

Not every male gay/bisexual pop musician of the 80s was visually marked by gender-bending, and not every male pop musician who teased out his long hair and wore makeup and an eyepatch was gay or bisexual. This allowed for a little plausible deniability. However, there were "out" gay and overtly political groups of the mid-1980s like Bronski Beat, whose album The Age of Consent listed the ages of consent for gay sex around the world -- highlighting the fact that the age of consent for same-sex sexual activity was five years higher than that for heterosexual sex. (The age of consent in the UK would not be equalized across gender permutations until 2000.) Bronski Beat's focus wasn't just on performing while quietly identifying as gay behind the scenes, or adopting alternate presentations with the plausible deniability that it was all for show -- it was on lyrics overtly describing gay experiences and on affiliation with gay causes. Compare the video and lyrical content of Frankie Goes To Hollywood's "Relax" to the video and lyrical content of Bronski Beat's "Smalltown Boy".

Female artists like Madonna courted controversy by allying themselves with gay causes and gay imagery -- but that controversy came from all sides. Is Madonna a gay icon and a friend to the gay community or an infiltrator, another big-name musician using queer imagery that isn't hers, like voguing? Is Madonna promoting homosexuality by mainstreaming and popularizing images of same-sex sexual activity, is her affinity for homosexuals and homosexual images a sign of her general moral turpitude? Other queer women (not merely queer-friendly) in new wave and pop, like Debbie Harry, largely flew under the radar -- not necessarily because they liked it, but because of overall image-control issues disproportionately affecting women in this era.

Meanwhile, on the harder end of the musical spectrum. The relationship of hard rock and heavy metal's long hair and makeup to queer gender transgressiveness is a little messier -- some bands were popular with gay listeners before they broke into mainstream acceptance, some musicians like Rob Halford of Judas Priest were and are indelibly associated with gay fashion styles like leather that project masculinity rather than gender-nonconformity. But other groups and musicians enforced their essentially normative position underneath all the makeup and teased hair by expressing casual homophobia, and by complementing their gender-ambiguous appearances with outsize sexual lyrics and images depicting women. In fan publications of the 80s and 90s there was a small war between female fans who derided more done-up bands as unmanly and female fans who defended them as essentially manly and essentially sexy. Therefore, it wasn't gay -- it was about done-up women being attracted to done-up men, and vice versa. There were gay men and women involved in rock and heavy metal, both as fans and as performers, but the comparatively more hostile climate made affiliating oneself with queer identity publicly more fraught.

Basically, while the 1980s had an apparent abundance of gender-nonconforming pop stars and gay celebrities who were out to one degree or another, it was still pretty hard to be gay in the music industry or in society at large. A gay man's album being at the top of the charts or homosexuality being chic in the world of pop music is no substitute for all LGBT people being offered equal rights and protections under law. Still, the number of openly gay public figures (including musicians, actors and actresses, models, writers, etc.) in the public eye increased markedly from the 1960s to the 1980s and hasn't really stopped since. In some ways, this was caused by increasing cultural openness toward homosexuality and advances in gay rights making it safer for gay performers to even tentatively engage with non-normative appearances and performances in public, and for audiences (gay and straight) to listen to and watch those performances; in other ways this increase was the engine of that new openness, increasing the visibility and accessibility of other non-hetero ways of being.