This might not be quite what you're looking for, but Syncthing[1] is a popular P2P file sharing solution. You could use Restic to make backups to a shared Syncthing folder.
Thanks for the suggestion. I've tried Syncthing, but it seems to still require that users are explicitly added (i.e., no public access [1]). I'd prefer a solution where anyone could decide to start helping replicate backups, without me having to add them in some way.
As far as I know, IPFS objects are immutable. Is your suggestion that I publish some sort of index containing all of the IPFS links to my backups, and then my friends can automate pinning those links? I think that could work, but it would be pretty bandwidth intensive since there would be no deduplication (I'd have to also encrypt since I wouldn't want everyone to have my files).
I'm not suggesting anything specific. Personally, I think allowing permanent public access to your server backups sounds like a terrible idea, but it's your data and you choose your threat model.
Crashplan home used to support this, but alas I've found no me alternative.