DDoS attacks could be considered forcefully shutting those mouths, and I don't agree with that. Do you propose forcing a private entity (Cloudflare et al) to publish those they disagree with?

You raise a very good question. We agree that DDoS is the digital equivalent of forcing someone to shut up, and that is contrary to freedom of speech. It's also true that private entities don't have any legal obligation to honor freedom of speech. Certainly you or I would not enjoy Instagram more if there was a bunch of hate speech on it.

But we can make a distinction between destinations, like Instagram, and infrastructure, like streets and public parks and libraries that allows you to access the destinations of your choice. DDoS is something that kicks people off of the very infrastructure of the Internet itself, thus denying others the choice to visit them.

The underlying problem is that core Internet infrastructure is managed by private entities. This is unlike "meatspace" where there are public spaces protected by the police / government who block the physical equivalent of DDoS (duct taping mouths / burning down printing presses). So, what does this mean as more of our communication as a society moves into the digital realm? Is it a blessing that it is more privately managed, empowering those managers to block "bad" speech? Or should we extend the same "meatspace" principles of free speech for all by requiring Internet infrastructure providers to provide unimpeded access to all?

Part of the problem with this is that on the internet, extreme ideologies have a reach that is impossible and hence manageable in "meatspace".