I would have absolutely no problem with it. The problem is this, why would they be changing his skin color, to appease a certain demographic? To make a statement hey we love them black folk? Or just cause hey we haven't reinvented this character in forever wouldn't it be cool if we did, maybe get people back into comic book reading, or create a new generation of fans with a new character or reinvented one.
Batman is Batman, doesn't matter if he is Latino, Black, White, Asian, or middle eastern. He fight for justice, not affirmative action, so who gives a fuck about his skin tone.
When they did make Spidey black/Hispanic and Bi, it was completely obvious what there underlying reason was. A big stamp of approval from the ACLU and LBGT community. It wasn't a natural progression, it wasn't a reinvention, it was a statement yelling at the top of their lungs, hey look at us we are tolerant. That shit pisses me off, and is completely retarded in my opinion.
As far as batman being black, sure do it, I'd like it if they rebooted the whole series, would give me a reason to start collecting the comics.