Ironically, Shakespeare doesn't need much changing. He has a pretty comprehensive suite of strong female characters, often stronger than the men in their plays, and he even has a major play whose title character was an ethnic minority (Othello). There's also a fair bit of LGBT innuendo that isn't really subtle at all.
Plus, if you're doing a modernized adaptation, for many of his characters, their gender or ethnicity really don't matter. It isn't integral to the story at all, and while the setting in his era may have justified certain tendencies, setting the play in another era negates that.