A 12" remix of a previous answer:

In a 2008 oral history of 'YMCA' in Spin magazine, members of the Village People and one of their producers, Henri Belolo, explain the genesis of the song. According to David Hodo (the construction worker in the Village People):

It was 1977, and we were leaving a photography session on 23rd Street. Jacques Morali saw the big pink YMCA on 23rd and asked, “What is this YMCA, anyway? “And after laughing at his accent, we told him the Y was a place where you could go when you first came to New York when you didn’t have any money — you can stay there for very little. And of course, someone joked, “Yeah, but don’t bend over in the showers. “And Jacques, bless his heart, said, “I will write a song about this!”

The Jacques mentioned by Hodo is Jacques Morali, a French producer who was the (co-)writer and producer of all of the Village People's biggest hits; Morali was gay, and sadly passed away in 1991 from AIDS.

In the group itself, there was a mix of sexualities in the Village People, with some members identifying as straight, some being ambiguous in print about it, and some identifying as gay. For instance, another member of the Village People - Victor Willis, the lead singer of 'YMCA' - is notable for being quite insistent that he is heterosexual; he married the actress who played Clair Huxtable on the Cosby Show. Willis has a co-write on the song, and Randy Jones (the cowboy in the Village People) says in the Spin oral history that:

It was not intended as a gay anthem. Do you have the lyrics in front of you? There’s nothing gay about them. I think Victor wrote the words, but it’s all a big fucking mystery. The guy who really deserves the credit is Horace Ott, who arranged the horns and strings. Jacques had the ideas, but Horace transformed them into songs.

In contrast, Hodo says in the same article that :

“Y.M.C.A.” certainly has a gay origin. That’s what Jacques was thinking when he wrote it, because our first album [1977’s Village People] was possibly the gayest album ever. I mean, look at us. We were a gay group. So was the song written to celebrate gay men at the YMCA? Yes. Absolutely. And gay people love it.

According to a 2013 analysis of the song and the relationship between the YMCA and 1970s gay culture in The Believer by Nicole Pasulka:

At the Y, a spiritual man was a well-built, muscular man. The organization’s leadership positioned the regional branches as destinations that could protect newcomers from “negative” influences. It was here that many young guys had their first homosexual experiences. So Jacques Morali and Randy Jones were part of a history that included both diligent Christian bodybuilders and men cruising for “trade”—straight-identified, masculine men.

Pasulka and the Spin oral history both portray the YMCA as a place with an official anti-homosexuality policy, but a culture where homosexuality was often common. Pasulka also portrays the YMCA culture as becoming less gay towards the end of the 1970s, and becoming closer to mainstream culture, comparing it to the Village People's acceptance by the mainstream.

By all accounts, in a world where much of gay culture was very underground, the fairly obvious gay subtext of the Village People to modern viewers was less obvious at the time to the mainstream - there wasn't much public knowledge about what Pasulka calls 'clone culture'; gay stereotypes at the time were very feminised. In contrast to the feminised stereotype, the Village People cast a knowing look at heterosexual masculine stereotypes with their choice of dress - cowboys, construction workers, etc - and the knowing look was missed by a lot of the mainstream at the time. This meant that the Village People could deny the gay subtext was there when they felt it was appropriate - and for Victor Willis who may have written some or all of the lyrics, there really might have been no gay subtext.

According to contemporary reports, the YMCA floated suing the Village People for defamation because of the implications of homosexuality, but didn't go through it - in the context of 'clone culture' etc, and Willis's denials of homosexuality it would have been quite awkward to prove. In contrast, the YMCA is now more relaxed about the gay overtones; their media relations manager said to Spin in 2008 that "We at the YMCA celebrate the song. It’s a positive statement about the YMCA and what we offer to people all around the world."

As to why a room full of 13 year olds at a church gathering would enthusiastically dance to the song in later decades, the Spin oral history notes that, by the 1990s, the song began to be used in sports settings in America, encouraged by team managers and the like who thought the song would be a crowd pleaser. According to, for instance, the director of stadium operations at the Brevard County Manatees:

There are a handful of songs that just make you get up and dance. At our ballpark, “Y.M.C.A.” has to be considered one of them. “Y.M.C.A.” is a gay song? Honestly, I had no clue.

'YMCA' certainly isn't the only song with an origin in or links to gay subculture which has become a successful sports song; Queen's 'We Will Rock You/We Are The Champions' and Frankie Goes To Hollywood's 'Relax' both come to mind. Perhaps there is a story there about the cluelessness of most sporting people around the cultural clues surrounding music; things that are very obvious to people who are engaged in the culture of pop music often slide past the heads of people who are much less engaged in that culture.

But of course, pop music by its very nature is there to be used, and the people who make pop music generally hope for it to appeal to as big an audience as possible. Whether Hodo's claims about Morali's inspiration for the song are accurate, Morali very clearly produced the song to be a commercial hit. And to be popular, pop music generally has to provide something useful to more than one group of people, as there are always different groups in society who are consuming pop music; songs without a mass appeal amongst different demographics tend to not have...mass appeal.

'YMCA' has - and has always had - a multitude of uses beyond 'celebrating the closeted homosexual interactions occurring in 1960's 1970s Christian gymnasiums'. It would never have gotten to #1 (in the UK, Canada, Australia, and much of Europe) or #2 (in the US) if that was its sole purpose - at least some of the places where it was successful would not have understood the meaning of 'YMCA', let alone the overtones of sexuality. After all, the song is very danceable, with a four-to-the-floor disco beat that works very effectively. It has easily replicable dance moves that are fun to do. It's clearly catchy. Victor Willis's vocal performance is strong in a soul shouter kind of way. The costumes of the group are memorable and their dancing is interesting to look at when you see the video. It also fit squarely within an extremely popular genre - disco - which dominated the airwaves and the charts in the late 1970s, to the discontent of the rock audience shouting 'disco sucks'. It's entirely unsurprising that it was a worldwide success in 1978.

Peter Shapiro's book Turn The Beat Around: The Secret History Of Disco claims that the Village People were:

practically personae non grata in the gay clubs. Instead, the Village People got most of their play at aerobics classes for senior citizens who could perform the accompnaying dance to 'YMCA' without taxing their bodies too much, at barbecues by car mechanics who thought 'YMCA' was about playing basketball, at strait-laced high school proms in Kansas and at children's playgroups. It was Middle America that took the Village People close to its bosom".

The Village People, in some ways, have stayed in public consciousness as an avatar of the cheesiness of late 1970s disco - disco has a reputation for cheese, and the Village People were pretty cheesy even for disco. Peter Shapiro's Turn The Beat Around: The Secret History Of Disco is scathing about the group: "if disco had a nadir it was unquestionably the Village People. The Village People represented everything naff about disco: the stale beats seemingly phoned in by studio hacks, the dunderheaded English-as-a-foreign-language lyrics, the complete lack of subtletly, all delivered by [a bunch of stereotypes]". Shapiro, of course, is attempting to rehabilitate the critical opinion about disco in this book, to explain its import and meaning, and he is intent on showing that disco had a smarter, more cosmopolitan side than you see in the Village People. Nonetheless, he also admits that - even if they're a harmless novelty act - the Village People have a 'goofy pleasure'. And who can deny some harmless goofy pleasures to a bunch of 13-year-olds?

/u/hillsonghoods has an utterly awesome answer about the history of "Y.M.C.A" that addresses your specific question at the end.