In the long term, excessive use of duct-tape labels works against you. Because they keep talking to the public anyway, while you've cut yourself off from the only thing that can give you a clue about what's going on in their heads.
Iterated prisoner's dilemma games [1] give us a good idea of how "liberals" (in the author's rather academic usage, not the popular usage) should deal with people who harbor other kinds of ideas: whoever tries to stop the discussion first, loses. You keep civil and engage their ideas publicly as long as they're still talking and not shooting.
Only when they do something other than talking that causes harm, you retaliate in kind. Violence (arrest and imprisonment) for violence (murder and other violent crimes), and political action (protest and civil disobedience) for political action (unjust legislation). But if all they're doing is speaking, the only way you can retaliate is with more speech.
If they're doing plain ol' demagoguery, well, isn't that despicable? You counter with better demagoguery. Thinking you have a better product is no excuse for poor marketing, and this applies to the marketplace of ideas as well. If you try to silence your competitors first, there goes your moral high ground -- the only high ground you might ever have had.
[1] https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#The_itera...
