I can't say I know for sure, but there isn't much opposition (if any) to my knowledge. There are some African-American re-enactors who obviously are fine with it--there might be some others who are uncomfortable with it, but I can't ever recall hearing anyone getting upset about it. Odds are there would be someone, I guess, but...
In the media, the re-enactors are pretty much always presented as a brotherhood, a bunch of guys getting away to go camping for the weekend, possibly have some bourbon around the campfire, I imagine, and maybe getting a little weepy together at some point (again, my imagination). Actors on each side will talk about how they respect each other and the soldiers that fought, and how there's no partisanship, etc. to the point where it probably doesn't need to get mentioned anymore if the TV coverage is just a brief little snippet.
I could be wrong, but if anyone is upset about it, they are for some reason not protesting or getting news coverage. Using my imagination again, I sort of wonder if an African-American watching re-enactors on TV, or stumbling on them on a weekend country drive, might see a bunch of guys in Gray running around, a bunch of others in Blue running too or whatever, then some shooting, some guys from each side fall down, and, what the hell, I guess that's what happened.

