El Capitan: After upgrade Mac won't connect to CardDAV-server
Something is clearly broken with El Capitan and CardDAV, but I could make it work by:


properly set up the standard /.well-known/carddav and /.well-known/caldav redirects (see your CardDAV server documentation to see the destination URL)
use the Manuel settings type - there are now 3 types of CardDAV configurations in El Capitan: Automatic, Manual and Advanced. In my experience Advanced is really broken in 11.11.0, but Manual can work with a server configured as described in #1