I don't object to references to raping my daughter and leaving her in a bloody pile in a ditch because it's politically incorrect.
No, but you also don't issue a press release saying how the entire community is just aghast at the whole business and how you're going to host a conference to talk about "healing", do you?
If they said something sufficiently heinous, you might try to track the fucker down and kick his ass (i.e. how "talking shit" was generally handled up until around the 70's), or perhaps something like Curt Schilling. In other words, a response based on going directly after the perpetrator. Direct threats are something for law enforcement to handle.
A "politically correct" response, on the other hand, is rooted in the idea that all we need is a bit more education and a lot more censorship.
Education will probably work in the very long run, unless it's so ridiculously heavy-handed that it becomes parody and propaganda. Censorship will work for a short while until the next mole pops its head up. The gaps in between the short and long term is where the trolls live.
I don't know what the ideal solution to trolls is, but I'm positive that ineffective hand-wringing isn't it, nor is trying to engage them in healing dialogue.
I'm pretty sure that effective, but not excessive, discipline where they can be caught is one necessary aspect (we tend to fail pretty badly as "not excessive" when discipline actually happens). Having society be just generally more resilient to offensive (and particularly anonymous) speech is absolutely critical.