Further, does espousing an anti-democratic idea make someone alt-right? How sticky is the label? What if you did it 10 years ago? Especially with how much of our lives we record nowadays, an accusation like this becomes an easy-to-wield cudgel to shut down political opponents. This rapidly leads to a race of gotchas, where we look for anything that lets us cram someone into one of the "bad" labeled boxes(racist, sexist, alt-right).
Lastly, how effective is the censorship you are proscribing? Can you achieve total censorship within the scope of a democracy? Does it actually inhibit the spread of the ideas you loathe, or simply put them out of your sight? What about the radicalization you are causing by censoring these people? You haven't convinced them to stop, you've just muzzled them publicly, but they can still create private clubs and gatherings. What problem have we solved after implementing this censorship?