There are several black characters, but they're all miner (lol see what I did there) NPCs.
When I played FFVII as a child the only part that freaked me out was the section with Mukki in the honey bee inn. And that wasn't because I was homophobic, but simply because I didn't expect it whatsoever and interpreted it as Mukki sexually assaulting Cloud. The cross dressing to me as a Brit (We have a history of laughing at male actors dressed in women's clothing), was simply comic relief to make up for the more serious tones the Game had beforehand (Barret stating the Planet's dying within the first 5 minutes etc). The cross dressing was also necessary to advance plot and unoffensive in NPC reaction. Barret's persona came across as more stereotypical and energetic than Racist, but to me Racism is only important when it has negative connotations, basically I don't believe Square wanted to have people believe all Black people speak as Barret does, instead they wanted to get across he's very passionate to the point of sudden anger, but perhaps I'm wrong, it's hard to find motive in an action. There was never a point to me when Tifa was sexually represented in any way in the game, Women have boobs, some big some small, maybe if every female character had large tits it'd be a misrepresentation but for Tifa it was only mentioned in the fandom. Cid and Shera was explained later in the story and her submissive behaviour too, was explained. Also let's not forget about the Cloud/Barret date scene, which again was comic effect. I doubt there will be many changes to FFVII myself in those areas but who knows? I for one didn't really desire a remake, why remake an already established masterpiece? Not to be cynical, it may be brilliant, but I can imagine nostalgia and such will win over the remake, and it will be forgotten soon or moaned about by the more obsessive fans. But anyways, PC culture having an effect on the remake? I doubt it. :3