One idea I've had is a content-type-restricted network that permits only text. That would allow utterly un-censorable communications: chat, planning revolutions, whatever, but wouldn't be useful for CP. (Unless you like ASCII-art CP.)
It could support ANSI. That would be neato. It would feel like the old BBS world. Wonder if anyone would still care if a name like ViSiON-X were stolen for it. :)
* You can base64 encode any file, so it'll look like text. Limitations on message size might solve that.
* Sometimes, photos and videos are important. Think of the Abu Ghraib torture pictures, the Tianamen Square Tank Man. Sometimes photos & videos are censored and should be shared with the world.
Maybe binary content propagates differently. Text that meets certain criteria is replicated indiscriminately, but binary content is only replicated when a user votes on it.
Edit: you could apply game theory to this problem. Model the network as a graph and write an agent-based modeling rule set for... say... CP-propagators and non-CP-propagators. Run iterative simulations of different propagation rule sets and weightings/parameters. Now introduce bad actors in the form of, say, government agents trying to suppress political discourse. The difference is that average-joe will cooperate in pushing out CP but will "defect" in a game with the other kind of bad-actor. You're looking for rule-sets and parameters where the CP gets pushed to the margins of the network or excluded but where the other kind of bad-actor is also excluded.
Could Bayesian classification be implemented through a homomorphic cypher?
If the encoding schemes become so obscure as to not be recognizable, then the problem is still effectively solved.
Usenet shows this kind of thing in action. It's now used for the most part for illegal file trading.
It doesn't get rid of them, but that's something that we wouldn't really be able to do (they all existed prior to the internet), but it would make the darknet usable.
It would be possible to encrypt text in such a way that things could be said about its information density but not about its meaning, too, though that would permit steganography to be used. But it would raise the technical bar for using the system for this purpose so high that it would probably drive away all the chickenboners.
There's also a dumb way: length limits. That would force binary data to be divided up into a huge number of posts, making it an annoying medium for file trading. Plotting the Iranian revolution would not require >1mb posts to a forum.