How about we do something silly like letting the police and justice system handle things like "credible threats of mass violence" and "hate crimes", since both are fairly illegal, at least in the US.
History tells us quite clearly that extra-legal justice systems as a response to even some of the worst justice systems creates more problems, not fewer.
So no we shouldn't, to use your phrasing, react as we see fit. That's how humanity has historically justified lynching.
Tell that to people who are now without jobs because of witchhunts. Jobs which are required in our society to have food on the table, a roof over your head.
Some folks who have been dropped from Twitch thanks to mob justice - where there's no actual crime - can't find a job in the entertainment industry anymore. Imagine being completely blacklisted from your industry because you were reported to have made someone uncomfortable (whether it actually happened or not).
Google never forgets, and people never forgive.
EDIT: To me, politeness doesn't make up for encouraging vigilante justice. My state has a long history of vigilante justice, and it's not pretty.
You're still misstating the issue; the "justice" in question isn't being executed by "vigilantes". It's a reaction of large institutions to someone's conduct.
That's because I see zero difference between an institution and a mob of individuals. It's still extra-legal justice handed out by people. One simply does so while also holding a business license.
EDIT: To be concrete: Pinkerton's (a corporation) was just as bad as the lynch mobs.
How is losing your livelihood, potentially being blacklisted from the industry entirely, not commensurate to judicial punishment? That’s exactly the sort of punishment we impose on computer hackers.
Why do you think jail is the only punishment doled out by the judicial system? As I just wrote, we ban computer hackers from using computers for life - that's not jail. ~Cancellation~ exile was a preferred punishment, also not jail. We currently sentence people to community service and other metered, lesser acts of contrition/penance/punishment. For instance, we make graffiti artists clean up their art with soap and water (still not jail). Another favored punishment is the fine, in which society confiscates ill-begotten proceeds or perhaps resorts to mere punishment as recompense.
I don't see much of a difference between a judge issuing a fine and an Internet mob merely destroying your life besides due process.
What is the record of our corporations? When did our multinationals become paragons of moral virtue and arbiters of righteousness? Do you think companies will only do things you like with this new found power?