So because some people choose to express their democratic right to disagreement for their own reasons, and this includes doubt about vaccines, the idea of being against vaccines should be treated as extremism to be forbidden? If that's your interpretation of how personal rights and free expression work in a democracy, then I fear for the direction of democracy with idiots such as yourself guiding policy.
As for what happened on January 6th, it was in practical terms a concentrated bit of aggressive protest theater, and far from anything seriously resembling an attempted coup. You'd have to be deluded by ideology to call it something so serious. For example, that event was much smaller than the enormous amount of government property damage and calls to topple governments made by a much larger number of people during the earlier Floyd protests across the US and other countries. Would you call those extremist too?
In any case, by naming the most radical actions of a certain subset of a wider belief system as a reason for considering all aspects of that wider belief system as extremist and worthy of banning, you're just another garden variety autocratic monkey at heart, looking for ways justify banning whatever concept doesn't fit your tribal identity.
By your ridiculous logic, any belief system could be justifiably banned because in some ambiguous way, it's "responsible" for the specific activities of certain people who hold to its most extreme version, though the two things (a wider system of beliefs and specific people's active choices) are separate.