When is it morally acceptable to contact employers in order to report something you’ve seen on the internet? I’m tempted to simply say “Never.” As in, it is never okay to attempt to transform internet drama into a potentially career-impacting catastrophe.
Certainly it was not okay when Greg Laden complained to the chair of Abbie Smith’s academic department over the content of her blog’s comment threads. Nor when a YouTube personality styling himself “Mykeru” rang up the University of Minnesota at Morris to complain about one of their professors. Nor when the Skepchicks publicly smeared an employee of a certain medical facility in Seattle, tagging and notifying her organization in the process. Nor when gamergate activists started a mail campaign to Intechnica in order to put pressure on one of their employees who was instrumental in creating the lamentable (but legal) Atheism Plus Block Bot.
All of these examples of employer harassment involve employees who were clearly not acting in their capacity as such, and all of them come with badly constructed ad hoc rationalizations in order to excuse what ultimately comes down to (cyber)bullying attempts to curb someone’s online behavior by threatening their livelihood. I’m quite confident that other examples abound, these are just the handful that spring to my mind where atheist or skeptic activists were somehow involved.
If I stretch my imagination far enough, I can envision scenarios in which turning someone into their employer is probably the right thing to do, for example, if they were leaking government classified (or corporate proprietary) information online or using their employee status to commit significant ethics violations. If, for example, an employee of a government organization made use of their web presence in order to promote a specific sect or religion, that would be a constitutional breach surely worthy of reporting.
The crucial question we have to ask ourselves is whether someone is doing something on their own time or whether they are doing something seriously unethical which directly affects their employers. The latter sorts of events are so rare that I cannot think of any community-relevant examples at the moment, but you are welcome to provide your own in the comments.