There's this wonderful Slate article about the history of that gay subtext that I'll be quoting from heavily. In it, the author quotes Grant Morrison:
"Gayness is built into Batman. Batman is VERY, very gay. Obviously as a fictional character he’s intended to be heterosexual, but the whole basis of the concept is utterly gay. I think that’s why people like it. All these women fancy him and they all wear fetish clothes and jump around rooftops to get him. He doesn’t care—he’s more interested in hanging out with [Alfred] and [Robin]."
As the article explains:
"from the opening page of Robin’s debut story in the April 1940 issue of Detective Comics No. 38 featured an introductory scroll jammed with breathless declamatory copy about “THE SENSATIONAL CHARACTER FIND OF 1940 … ROBIN, THE BOY WONDER!” It began, “The Batman, that weird figure of the night, takes under his protecting mantle an ally in his relentless fight against crime …”
"Or at least, that’s how it was supposed to begin. But the page’s letterer, tasked with squeezing a hell of a lot of text onto said scroll, unwittingly shoved the words “an” and “ally” so closely together as to effectively elide the space between them. Thus, the first thing readers ever learned about THE SENSATIONAL CHARACTER FIND OF 1940 was that he was someone whom Batman “took under his protecting mantle anally ...”
"Queer readers didn’t see any vestige of themselves represented in the mass media of this era, let alone its comic books. And when queer audiences don’t see ourselves in a given work, we look deeper, parsing every exchange for the faintest hint of something we recognize. This is why, as a visual medium filled with silent cues like body language and background detail, superhero comics have proven a particularly fertile vector for gay readings over the years. Images can assert layers of unspoken meanings that mere words can never conjure. That panel of a be-toweled Bruce and Dick lounging together in their solarium, for example, would not carry the potent homoerotic charge it does, were the same scene simply described in boring ol’ prose."
Everyone has been aware of the subtext since Wertham, with DC and later the TV show going out of their way to add female characters to Wayne Manor. But when George Clooney appeared on movie screens with bat nipples, well...
Maybe it's not our business what happens with consenting adults. And if you don't think Moore would agree, maybe you need to go track down SMAX.