I guess I'm not familiar with all the details. To me, I understand that Alex Jones is/was being demonised because he indicated that the plaintiffs couldn't answer legitimate questions to demonstrate that the Sandy Hoax shooting really happened, and therefore postulated that the story was a lie. The fact that some insane woman gave death threats should be treated entirely separately - there are plenty of liars in American politicis, but death threats are never seen as a legitimate or lawful response to resolving the problem of liars.
Did Alex Jones actually bully or harass the grieving families? Or did he simply exert his First Amendment protected free speech right to indicate in the press that he believed the families were lying, because of contradictory and/or absent evidence used to support their claims? My understanding is that it is the latter.
This emotive response is unnecessary and scripturally inaccurate. Jesus died for sinners, and it is not an unforgivable sin to be mistaken. My understanding (again, not perfect), is that if the families actually were able to provide the evidence that the event really happened, Alex Jones would not have come to the conclusion that the event was a lie. Instead, the families appeared to respond emotively rather than logically, which is a typical response from liars when they get caught.