If 10 people on the internet tell you they want to kill you, how do you tell if 1 of them is serious and is actually going to show up physically?
The answer is that you can't, and there isn't a firm line where all trolling is on one side and harassing/violent behaviour is something different.
Many of us can heuristically decide that trollish behaviour aimed at us won't extend to our person/home/workplace, and doesn't need to be taken seriously. That doesn't mean it's a rule for everyone or an excuse for that behaviour.
Yeah, no, that excuse stopped working around six years ago. “Online trolling” is now part and parcel of political action and can be separated only through naïveté or disingenuity and no, there is no third option. The shitlord who chased my friend from her home was cheered on by that faceless mob of “online trolls” and encouraged other people to do likewise and worse. Similarly, Elliot Rodgers and the like got their book from “online trolls” who happened to also be virulent misogynists who were ecstatic that somebody took what they advocated and put it into action.
What you call “extreme” is the reality for people less privileged than you being subject to these fucks’ weird jollies. What’s your just-ignore-it stuff going to do for them?