Allow all users of a group to start and stop zope using supervisorctl

Take a look at unix-http-server section. Change your configuration file as belows:

[unix_http_server]
file=/tmp/supervisor.sock   ; (the path to the socket file)
chmod=0770                  ; sockef file mode (default 0700)
chown=zope:zoperun          ; socket file uid:gid owner
;username=user              ; (default is no username (open server))
;password=123               ; (default is no password (open server))

This make the socket file can be read, write by users in zoperun group:

ll /tmp/supervisor.sock 
srwxrwx--- 1 zope zoperun 0 Sep 30 16:54 /tmp/supervisor.sock

Finally, add all users you want to allow start/stop Zope instance into zoperun group and testing with normal user, you will see something like this:

$ supervisorctl status
foo                              STARTING