If you do really want true anonymity and un-censorability as guarantees of the system design, then no, I don't think users can decide what they don't want to store or transmit. For, if they can, then their governments can coerce them into making the same "choice." Any preference that can be set by a user, can also be forced upon said user by a system administrator, operating system vendor, etc.
My real question is, do we need cryptography and anonymity built in at a protocol level to have something that's useful for political activism? It seems to me that there are only two real "innovations" these networks bring over, say, pushing encrypted blobs to people over SFTP drops (these, by coincidence, are both factors I've only really seen on Freenet):
1. That you have the ability to "push" content into the network, such that it will then replicate and spread through the network as it is accessed, without the possibility of an audit trail leading back to the source peer (even though the original source may know which client uploaded it, each peer only knows which other peer they got it from, so all you need to ensure anonymity is an internet cafe);
2. That content cannot be removed from the network easily--as there can always be dark peers who have copies of your data block, who will come online later and repopulate the network even if it has been seemingly purged of a block (by, say, all involved homes and data-centers being raided by the feds)--and that this happens pretty much transparently to the people involved, since people are always joining, leaving, and re-joining the mesh/swarm/whatever-it-is.
Encryption need only happen on a layer above this system, where and when it's desired. Anonymity need only happen at the end-points: the users can just access the system over Tor if they don't have the requisite internet cafe/seven proxies handy.
As long as you're just passing cat pictures around, why not just throw them onto a simple, infinitely-sized, everyone-can-create-files-but-nobody-can-delete-them DHT-based "disk"? And if you're passing political activism around, just encrypt and sign it like you were going to send it over email, then drop it in the mesh and email the URN instead. (This is presuming a stable PKI key-publishing/querying infrastructure as well, of course.)
And if you want to make it convenient for end-users, just make a browser extension that can load those URNs through the mesh as if they were regular HTTP URLs, and does the decryption and signature-validation automatically--and have the mesh software install that browser extension--and then you'll have something.
The latter is basically equivalent to this system, and so your system would have exactly the same problems: the only way you could avoid being a relay for child porn is to refuse to relay any encrypted content, at which point your node is not helping the political activism. Allowing unencrypted content also leaves you much more open to traffic analysis (if only a small fraction of data is encrypted, it's much easier to find the nodes that are inserting the political activism data).
We can probably convince your mother to download an app from the App Store that integrates just with the lower layer--hey, it's just like Dropbox, but bigger! [Well, as long as anyone and everyone can read random samples of your data if they like...]--because the upper layer, with the encryption and signing, will siphon off all the stigma of not-so-above-board usage of the protocol and attach it to itself. It's no different technically, but it is very different socially.
The advantage of having one reviled app on a larger infrastructure is that that reviled app gets to "hide" its blocks among all the above-board usage of the infrastructure. Like another poster in the thread said, if you go onto Freenet or the Tor Directory, the links to CP sites are plain and obvious, because it's a large part of what's going on there. But if you could look at your own disk usage as a node in this network, I imagine the number of encrypted blocks as compared to, say, plain-old MPEG frames of TV shows, would be vanishingly small. (And it's be relatively impossible to define which is which, either, since this infrastructure has no "index" or metadata; it merely is a big bucket of blocks named by their content hashes, of which most--not just the encrypted ones--are meaningless unless you have another block giving the order in which to string them together to make a file.)
† "Anonymous, Uncensorable, Ethical: pick two."--named after the CAP theorem of database design. Well, it would really be the AUE conjecture for now--but I'd love to see someone prove it either way; it seems like the sort of thing that is amenable to that.
If you can't tell whether a given block is encrypted data or just part of an mpeg, how can you choose to store only unencrypted data? I suppose you could make an argument for building this system on top of a nonencrypting distributed data store, like bittorrent, for the sake of looking like that nonencrypted protocol to anyone intercepting the traffic. But there would have to be some metadata that let the encrypting protocol know where to find its stuff, and if the user who's downloading it can tell, so can anyone intercepting the unencrypted stream. Wouldn't you just end up with a situation where the upper layer is to the lower layer as freenet is to the internet?
I didn't say you could :) The point of this alternative is that it separates the stigma 1%-99% toward the upper layer, but puts the implementation 95% into the lower layer--and therefore we get a stable, un-censorable distributed storage network on the lower layer with the "abuses" of the upper layer (CP and political activism both) being an unavoidable free rider, but not something "visible" (in the sense of seeing CP sites listed in your index directory) to people only using the lower layer.
This situation, of course, also describes the Internet as it is today: protocols like HTTP and SMTP are used by everyone, and also by some unethical people who send their stuff over those same protocols in encrypted containers using anonymizing proxies.
The difference here is that the two big hurdles--of identity-diffusion over time after initial data seeding, and of guaranteeing data persistence as long as there continue to be consumers of the data becoming persistent-caching peers--are taken care of by the lower layer, allowing the upper layer to just handle transparent encryption in whichever way it sees fit.
(And thus can we also replace the upper layer if we come up with a better way to anonymously and securely get the right metadata into the right hands, without having to throw out the network effect of all the extant peers. They simply start transmitting-and-caching blocks representing the new kind of metadata exchanges along-side the blocks representing the old kind.)