While I agree with your general sentiment, free speech absolutism is meaningless in employment settings without something like militant labor organizing to defend it. It’s not protected in many cases and they can always just fire you and exhaust your resources in any resulting legal battle.

If you had a union on the other hand, it could stipulate protection of this kind of speech as part of the employment contract and marshal the resources to mount an actual, meaningful defense if your employer were to try these tactics.