Well, or they have a more nuanced view than "censorship no" or "censorship yes"
For example, I support laws preventing stores from selling 3 watt LED bulbs in packages claiming they're 5 watt LED bulbs; or selling generic LED bulbs in packages claiming they're Phillips bulbs. Even though the printed text is surely the manufacturer's speech.
Must I support all censorship, because I support this one bit of censorship?
"Hello, this is just a reminder that your voting station will be open between 5 pm and 9 pm in (somewhere where it's not actually located), please remember to vote!"
"Hello, if you would like a free ride to your voting station, please text us 'YES', and wait at (location) between X and Y pm (Nobody will show up)."
"Hello, we have a great offer for auto insurance, blah, blah, blah."
"Hello, just a reminder, millions of trustworthy people believe that <opposition candidate> was responsible for <something untrue and horrible>. This isn't slander, because we are just strongly implying it in this robocall. Also, they live at XY address, and won't someone rid is of this meddlesome priest?"
"Hello, all the doctors are lying to you, buy our snake oil wellness supplements, instead. They are supplements, not drugs, we don't answer to the FDA."
"Hello, let's go down to sixth and Broadway next Tuesday, and make some noise/put the fear of God into <group>"
"<Ethnic minority group> is burning this country's forests down using space lasers."
"Hello, please be aware that it's illegal to discuss your salary with your coworkers."
This is a terrible analogy, and evidence that the people who claim we can't protect all speech have no idea what "free speech" actually is.
Hint: no, it's not fraud.
Saying these bulbs have 5 when they have three is a lie but shouldn't be censored. Selling someone 3 but saying it is 5 is fraud. Selling/buying have different laws and standards.
I don't support any censorship at all for any topics even those that deeply offend me.
The only exception would be actual death threats and things that are illegal to do.
So people like this will say sentences like “censorship is wrong” but implicit in the sentence for them is “censorship of correct and/or my information is wrong” because the sentence in their mind must be concretely about something like “correct information”. There’s no way for them to easily think the thought “censorship is wrong in the abstract.”
This also feels related to being able to use “veil of ignorance” type reasoning. I don’t think they know how to imagine being not only a different person, but an unknown person.
I also don’t think they know how to imagine being wrong in some sense, not in the epistemic humility sense (although, yes, that too, much of the time), but in the “suppose I’m just deeply confused about everything, how would I want to be treated? How might I recover?”
I think all these are bottlenecked on a mental abstraction ceiling, and I think all these things work together to contribute to the effects you noted.
Think about what makes you consider "threatening speech" a "force": presumably it has nothing to do with particle physics... is it perhaps that the act of speech itself causes people to adopt behaviours they wouldn't normally adopt? ie.: that it can carry some coercive weight? That it can be used to exploit/endanger vulnerable people in some circumstances?
Speech may be a very very weak force in most (or even "nearly all", just for the sake of argument) circumstances, but there are tons of examples of speech being a powerful force, causing large social and historical shifts. There are both positive and negative examples of this.