First thing that came to mind reading the title was Laurence Olivier's Othello where he played the character in blackface for the whole film lol.
I realize this post is meant sarcastically but yeah, I mean, lets just not do that?
Its really interesting to watch old films IMO to get a perspective of the evolution and history of the art. Im a sucker for old classic films.
But wether its old classics or modern films, you can watch whatever you want and simply not watch a controversial film that touches a sensible vein to you. No one is forcing you. Lars Von Trier has been doing "controversial" films his entire career and its always annoying when they censor him in the USA like they did in Antichrist because, again, you can simply not watch the damn thing if you dont like it.
Just as you dont have to listen to music you hate, buy a modern painting you dont understand, watch a ballet that bores you, play Arms, etc, etc, etc