This seems to miss the point. There was a time when effectively the only roles black actors could play were specifically written as black characters, and given the small number of those, that some that might be construed as black characters, and the fact that actors blacked up to play Othello shows that it was one, were more likely to go to blacked up actors is even more problematic.
Again women suffered from a lack of rokes, and given the originals in Shakespeare were not played by women, a bit of readjustment now causes me no problems.
Both of those seem very different to the question of sexuality where there doesn't seem to be a restriction for gay actors.