Are there somewhat popular social networks that require commenters and posters to license their work under a free license (e.g. CC-BY-SA-4.0)? Then anyone would be free to create a "clone" of the website and even make derivatives, all without breaking copyright law.
There are many wikis like this (e.g. Wikipedia) and at least one forum (trisquel.info), but I don't know of anything for more general purposes. Even most fediverse sites, which implicitly grant permission for some specific kinds of mirroring, don't usually have a free license that allows redistribution in completely different contexts, as far as I know.