Have you considered that the disappointment might be of your own doing? I mean, it's kinda silly to act like an asshole and then feign surprise and hurt when you get treated like an asshole. Just sayin. You sound like one of those types who thinks free speech means freedom from criticism and disagreement.
But anyway, I would never write up any one of my reports for something where there was no proof or evidence except for an anonymous email. I would investigate the matter thoroughly and independently, and perhaps maybe even ask the employee why someone might make such an accusation, but would take no action without proof (or confession) of some kind. Taking corrective action against an employee without that isn't just bad management, it's setting yourself up for trouble with that employee, should the accusation prove to be false.
Based on your attitude displayed here, and your proposed 'solution,' I strongly suspect your story is BS. Propaganda intended to silence 'woke' speech you disagree with by casting it in an unlikely negative light.