The free flow of information isn't driving extremism, it's echo chambers. People have a tendency of surrounding themselves with only those who already agree with them on some topic, so that a heavily partisan position suddenly becomes 'moderate.' This is how you have people simultaneously claiming, for instance, that the US is becoming more liberal than ever, and that it's becoming more conservative than ever.
You can also see this with the perception gap [1]. Those who are most involved in politics tend to be the paradoxically least knowledgeable about what 'the other side' thinks and believes. Typical contemporary examples would be republicans thinking democrats want to defund the police, or democrats thinking republicans are against immigration.
When you have contrary ideas bouncing against each other, poor ideas are easily demonstrated to be such - and you get a more realistic view of what people 'on the other side' actually think and believe. It naturally tempers against radicalism. But when you start to control information, you get the opposite. This is made even worse by the sort of people that find themselves on a life trajectory to go work, let alone volunteer, for the 'Ministry of Truth'. They tend to be the exact sorts that want to create information bubbles and echo chambers.
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In general I think the truth tends to trickle up, even if it might get a bit dirty on the way there. I'd appeal to places like the USSR on that. They not only directly controlled absolutely all published information, but strictly controlled migration in and out of the country, informers everywhere making people terrified of speaking their mind, and just generally had a rock solid grip on information. The result? People still knew they were all full of shit. There's a great series of jokes from the era here. [2] On of my favorites, "Why do we need two central newspapers, Truth (Pravda) and News (Izvestiya) if both are organs of the same Party? Because in Truth there is no news, and in News there is no truth."
[1] - https://perceptiongap.us/
[2] - https://johndclare.net/Russ12_Jokes.htm