Public criticism can challenge authority but also improve trust. Should admins respond openly, move discussions privately, or ignore them? What approach strengthens credibility?
For me it depends on their wording and if it's an attack against the site rules, or just me personally. The Site Rules are not to be argued, in my opinion and I usually will copy and paste them into the thread. Attacks against me, I let the site owner or other staff handle it instead of doing anything, because I want to remain objective.
I would respond appropriately to it. When moderating, assume the position of law enforcement. Moderation is a lot like police work. After you moderate and you're criticized for it, then explain what happened in public as if you were a police officer explaining an enforcement action. Remain professional and don't get emotional. Don't lose your cool because it's just the internet after all.