Bruce Wayne's origin doesn't really have a racial component.
Well, arguably it does, because Bruce is supposed to come from old money, and the first African-American billionaires have only come along in the past few decades. So a nonwhite Batman would need some aspects of his backstory changed, say, have Thomas Wayne be a self-made business success rather than the inheritor of a generations-old fortune.
Then again, the idea that the Waynes are old money is itself something that's accreted on over time; I don't think it was originally the case. So if it was changed before, it could be changed again.
And just to clarify, I'm someone who's always been okay with the notion of a black Batman. Back in the '90s, when I fantasized about creating a new Batman TV series, I couldn't think of a more ideal candidate for Batman than Michael Dorn.