You can't censor away extremism or any other problem

No, just makes it edgier for the kids. Takes longer to crystalise but crystallises harder.

I think you have a point in that no one has a right to force me to listen to their speech.

However, I think that in the case of the monopolies being discussed here, it's different. The issue is that they "enable" speech in a generic way. They don't enable this or that speech in particular. They also don't force A to listen to B's speech. If anything, they do the complete opposite, what with the whole "echo chamber" situation. I think this is the whole meat of the "platform vs publisher" debate.

A newspaper or other media have to actively "enable" something. When they publish speech A, they choose to not publish speech B. It's often an "either / or", at least for questions of space. They produce whatever speech they print / show. It's theirs, it's their point of view.

However, Facebook, Twitter and other similar companies only put out a tool. This tool is then used by this or that person to speak this or that argument. FB doesn't actively and directly help speaker A anymore that they help speaker B. Also, as an FB user, no one forces you to listen to B's speech if you don't care for it. Your right not to listen to speech you disagree with is not infringed. If I publish a story on FB, it's my story, my speech, not Facebook's. Just as if I shout in the town square it's my speech that I shout. It doesn't become the mayor's speech because it's in his town or the square's architect because he built it in such a way that my voice can physically be heard.

If you consider that FB has some right to prevent people from speaking "wrong" views, then why stop at FB? We should come up with ways to help other companies to prevent their product from being used for speech and other actions they don't agree with. Like the power company. Maybe they don't like their electricity being used to spread some "wrong" ideas. I'm pretty sure the local bakery isn't all that happy either to support some X-ist fanatic.

Where do we draw the line?

Of course you can do it in theory. The question is, whether you can do it today and whether those attempts will turn out more dangerous than helpful. IT achievements allows for extremely easy exchange of the information throughout the world. You can easily circumvent many kinds of blocking. You have E2E conversations available to masses, so you can't effectively censor anything centrally.

Whether that's good or bad is for history to decide. Recently I saw some guy watching video about terrorists executing some prisoner. He got it via whatsapp. That video was pro-terrorist, they obviously are trying to recruit more people by spreading their propaganda. Of course I would prefer such kinds of conversations to be silenced. The thing is, it can't be silenced. Russia tried to block Telegram, they poured lots of IT resources, they used DPI and other methods but they did not succeed and did lots of collateral damage in the process by blocking innocent websites.

I think that genie is out of the bottle already and we have to learn how to live with it. IMO governments right now are trying another method: they put lots of disinformation, hoping that average folk won't find out which one is true. Not blocking specific information, but making it hard to find and distinguish truth from false. That works for me, I already stopped to trust most of the information on the web.

I think the extremes, both left and right, have realized that their greatest enemy is not the other extreme, but the masses in between.

A group that has the numbers, with mild views that can dilute your message with reasonable doubt, challenge certain aspects of your extreme yet be broadly acceptable to a much wider audience including those tending towards your side – that's poision for an extremist.

Therefore, their solution to that is tribalism, polarization, and shaming for any hint of non-compliance with the extreme's dogma.

End result is that the vast majority of moderate people do not participate in debates on sensitive topics, leaving the field open for polarizing demagoguery. All that's left is to make more topics sensitive to get an advantage there too, and that's progressing very well too.

When you elevate yourself above a group of people there is no option for dialog, because engaging in dialog would mean that you view those people as equals.