One major thing in the UK is that politicians complain often about people criticising them on Twitter. They read out the hateful tweets they receive with ill-disguised glee, and suggest direct moderation (already happening to a certain extent, in line with EU regs). Celebrities also push this line heavily, milking social media for advertising cash and complaining that their critics should be removed from the platform.
...I just don't get it. If you are interested in parallels, there is an interesting parallel with the introduction of the printing press to England. This spurred massive growth in political pamphlets which offered all kinds of fictitious nonsense about prominent people. Attempts at censorship failed, and that industry grow into news. We have been here before, we lucked out last time, we may not be able to do so again (censorship in China certainly indicates that govts have the resources to censor more effectively than ever before).