Except this isn't a "we should record everyone's interactions to stop terrorism" it's "we should stop hosting propaganda for terrorists, especially when that cessation doesn't harm others (dropping hosting for their website does't impair other people's liberties, whereas spying on everyone's messages would)"

In a courtroom you wouldn't get away with absurd hyperbole like this. It would hurt your case more than help. No wonder the activists want to avoid court and rule through social media where hyperventilating emotional blackmail is pretty effective.

It harms everyone. It harms yourself.

Either free speech is absolute or we can suppress the speech of anyone we don't like. At some point society will dislike you.