How is the impediment happening? If through the threat of violent or illegal action, then that should be illegal. If it's libel (false statement, made while knowing and believing that it is false, with intent to harm), then maybe it should be illegal too. Otherwise, it's protected speech.
Whether a thing is legal or not doesn't mean everything that stays within the legal bounds is desirable as a society or morally, ethically just. Many of the most atrocious deeds of humanity have been legal at the time they were carried out.
By saying all of this I am not doing myself a service here. Such opinions get downvoted on an US dominated platform like this one. I still think it is important to note that any freedom we are gurantueed comes with a duty to protect these freedoms for others. Those who enjoy a freedom and at the same time try to take that very freedom away from others can not complain if a free society tries to defend itself and limits their rights.
When thinking about how societies can stop aliding into fascism after the genocides of the second world war Austrian philosopher Karl Popper coined the term "paradoxon of intolerance" for this. Any free society that wants to survive, cannot be universally tolerant — otherwise the intolerant will abuse that "hospitality" and abolish that free society. That means any free society has to be intolerant towards the intolerant, after a certain degree. I would argue this degree has been reached in the US a while ago.
Protected speech is a strong word in a nation which killed civilians on foreigns soil based on what they have been communicating via SMS without a trial. Here, suddenly, it is okay to go after people based on what they say somehow?
I'm not sure how speech can impede on the right of others to speak freely. Speech can certainly discourage others from speaking freely, and that's bad for freedom of speech in a broad millian sense[1], but it's too vague to justify shutting down an entire forum because some speech there might discourage others from speaking freely.
If you think it wouldn't I'd like to know how your thinking goes. I am not from the US, so maybe the whole theoretical idea is different from the ground up.
You're right, certain speech, like direct threats of violence can impede on other people's right to freedom of speech. But such speech is illegal even in the US and also banned on Kiwi Farms.
Is it legitimate to take that platform down? You don't have to answer, the US certainly thought so during the past wars.
Is it legitimate speech to write some vague SMS to the wrong person? You don't have to answer, whole wedding societies have been killed for that speech.
Now one could argue, "Yeah but they might have been terrorists, or associated themselves with the wrong people."
But what is terrorism and why does a free society break it's promise of freedom of speech to fight it? Terrorism is trying to reach political goals by (often) violent means, with the aim to create fear. This fear stifles the free discourse in a free society by targeting specific symbolic targets. And isn't that a definition that fits many fringe political groups that would target individuals and make their lives hell like it apparently happened in the case of KF?
What if the freedom of speech you are defending is impeding on the right of others to speak freely?
While I agree with the sentiment, that we have to be especially observant how we treat the freedoms of the people whose opinions we dislike, I don't think just defending those and forgetting about the grand picture is in great service of freedom of speech as it stands.
Maybe this is my liberal (?) European bias, but I don't think for example there is much value in definding some extremist political group that goes after some other people whose opinion they don't like. In the worst case, you are defending a group who has a huge chilling effect on the free speech of the other group, by making them afraid of speaking publicly about their cause.