BuddyPress.org

@joshua_d Some other options include
https://wordpress.org/extend/plugins/bp-profile-privacy/
https://wordpress.org/extend/plugins/buddypress-profiles-manager/
and/or making the site private for members only via script or a plugins like
https://wordpress.org/extend/plugins/s2member/
https://wordpress.org/extend/plugins/hs-membership/

I know that there are other devs who are interested in developing the plugin. Just don’t know when it will happen and whether or not it’ll be free or premium.