BuddyPress.org

TLDR version: Introduce types of groups. e.g. “User group” type – it has no forum, no “Home” page, just members listing and activity stream. This group added to Activity Stream filters where relevant.

Would have to filter out custom group type “User group” out of the /groups/directory page & member profile group page.

These custom group types could be set so they are publicly visible/private to those members involved/or hidden (visible to the creator only). As per current Group privacy settings.

Could add e.g. “Friends”, “Colleagues” and “Fans” as default, empty groups for each user on user registration. Obviously revise theme to make the “Friends” page (“Connections”, maybe) look like the Friends page rather than a regular Group.

Different users might create “User group” types with the same name but with different meaning (“Fans” could be interpreted several ways for example). This is no problem as such categorisation is defined — and belongs to — the user who does it. Might need some semantic group kind/type identifier in the code to allow FOAF/SIOC RDF profiles to be able to assigned to these “User groups”.