When a random internet citizen directly approaches your company with the explicit request to fire a named employee, this by definition is insane.
The reporter is not interested in reporting a particular offense, instead they are already playing the executioner. They do not want a solution, they want punishment and retaliation. That behavior is both arrogant (not their call to make) and sadistic.
The reporter is not interested in what is best for your company either, as the "request" typically comes with threats. Comply or else...
The very nature of such requests means the reporter is the type of person to dig up personal information or old "offensive" posts, which is unhinged behavior. Likewise, the reporter was unable to come to a resolution with the "offender", so plays the snitch card instead.
It's a pile of red flags. Normal and reasonable people do not go after a person's job, even less so collectively. I wouldn't do that to my biggest enemy. That doesn't mean employees can't screw up, perceived or real. When they do, mob justice does not satisfy the very basic principles of justice. There's no defense, and without defense, there is no justice.
Most companies can safely ignore such requests. The mob has no patience nor are they typically a customer in the first place, so all economical threats are in vain. It's largely a temporary PR threat that is emotionally inflated versus the actual PR impact: close to zero.
Of course, I know, there's exceptions to all of the above.
I'd say it would be a good thing if there's legislation that protects against mob-triggered terminations. The reason I would opt for that is that mob justice goes beyond just the termination of a few. It has a larger societal impact in the sense that those few are to be seen as examples for other people to increasingly feel like they need to walk on egg shells: extreme political correctness, large silent majority, you get what I mean.