This would all be done by PM, and only in specific cases where remarks were still being made about someone in posts even after they had placed that person on their ignore list. I am definitely not in favour of politicising or dividing the forum any more than it already is, but sometimes the ignore list is a better option than allowing the conflict or angst to continue.
I would not permit such derogatory posts to be made once they were pointed out to me.
It's a shame that some threads end up like that, but I'm not going to pretend it doesn't happen. A little less dogmatism, and a little more respect for others goes a long way. I'm not speaking of anyone in particular, but in general. I think that everyone is aware that the sort of situation that you are referring to occurs almost exclusively in political and religious threads.