How do you handle negative feedback and protect your reputation online?

Respectfully: why? Why engage in the Karen-ification of the culture? Why validate the idea that everyone is OWED some guaranteed experience that aligns with their own preconceptions? Why elevate the pervasive-and-worsening sense of being aggrieved? Where is the acknowledgment of the risk inherent in seeking out a live experience of any sort - concert, gallery exhibition, comedy show, etc.? What's become of our collective capacity to attend something, conclude that it was not to our liking, and have it end there? Why - in a climate where resources have been dwindling for decades - must already beleaguered arts workers act as stewards for the mood state of every individual who comes in the door? And keep coddling them after they've left?

Don't mistake me: if someone has suffered mistreatment at your event, then it's obviously crucial to address this squarely. Or, if somebody takes deep offense about some element of production or policy to the extent that it constitutes harm, then it's vital to give its due. But this notion that everyone must LIKE everything they go see, and that if they do not, that they are reasonable to expect some form of redress from the makers/administrators of the presenting entity is deeply strange to me. It's an inversion of the dynamic between artists and audiences - the purpose of artists, in part anyway, is to lead audiences where they DO YET KNOW THEY WISH TO GO. This necessarily involves discomfort, upheaval, even.

This inversion will lead to gutless, focus-grouped seasons; audacious young writers, especially writers of color, will have their work relegated (even more than it already is) to "workshop hell," where the only daring or novel work theatres involve themselves in will be staged readings for a handful of fans who are already diehards. Theatre as a field will abdicate its obligation to LEAD, and instead catering to the existing middlebrow preferences of an aging audience that will die off without being replaced. Theatre's faltering hold on relevance will slip away. Pointless seasons crammed with "Christmas Carol" that fail to speak to the present moment since we'll have abandoned the attempt, but that swaddle us in false, familiar certainty.

To engage audiences deeply and meaningfully and (most important) lastingly will require that we articulate for them not simply "why we're presenting this play," but "why this play matters at all," "what in this play enlivens and ennobles us," "what needful challenges this play puts to us," etc. As the OP suggests, audiences need not AGREE with the choices an institution makes in its programming - I'd submit that a measure of dissent among ranks is crucial - but if we are tepid and mild and unimaginative in our defense of our work, we will be complicit in our own undoing.

Take accountability! Use the criticism to reflect on what can be improved upon; list out how you are going to make changes and actually act on them. Regardless of the severity of the situation, taking accountability is the no.1 surefire way to protect your reputation and keep the respect you earned as a SM.