They should and they already do. Spreading misinformation can be classified as terrorism. Saying that there’s a man in the sky should be ok; Asserting that there are chips in vaccines is a matter of public safety. Someone will avoid getting the vaccine and die as a consequence of that post.

As for the punishment, it could be as simple as community service or losing access to public benefits for some time.

“Doctors are killing people with the vaccine?” Ok, find and pay for your own doctor, you’re not welcome in public hospitals.