Now some will argue that's political correctness. I do think, however, that such stuff should not be shown in PG-13 movies. I think lynching is serious and any movie that gets an R for detailed depictions of lynchings deserves the rating in my opinion. It would send the message that lynching other races is wrong.
Lynching is serious, but so is murder for any other reason. How is religiously motivated murder any different? Lynching other races is wrong. What does that have to do with anything? Just about every movie contains something that is wrong. Murder, rape, profanity . . . The Hobbit, for example, had a PG-13 rating despite the fact that those elves killed about a million orcs. Also, the orcs are trying to kill the hobbits and the elves for the simple reason that they are hobbits and elves. If that isn't racially-motivated killing, then what is?
Suggesting that movies should be punished for portraying immoral behavior is illogical. Every movie contains immoral behavior. The clarification should be made that movies can contain immoral behavior without condoning and promoting it, which, in the case of lynching, does not happen anymore. Lynching is always portrayed negatively, at least in the case of racially-motivated lynching.
On the other hand, excessive violence (in the form of lynching) should get an R, for the same reason other movies with other forms of excessive violence should get an R.