I actually thought the Jack Sparrow was pretty heterosexual in the movies, but then I don't work for Disney:
Depp talked about it in an interview with rocker Patti Smith for the January edition of Vanity Fair magazine. Depp said Disney "couldn't stand" his Sparrow and one person there even asked if Sparrow was gay. Depp told the Disney executive "all my characters are gay," and he said that "really made her nervous."
I doubt their target audience was thinking that Sparrow was gay or supposed to be gay or anything like that. Heck, he didn't even get the attention of Jerry Falwell, who was alive back then, who thought everyone was gay.
But that's Hollywood, especially the corporate, "family" side of Hollywood: they beat Jerry Falwell at his own silly game.