2 issues want to describe here.
FIrst one:
The recent version of Thunderbird (version 38) changed the behavior and now issues the command:
list (subscribed) "" "*" return (special-use)
This command doesn't return any folders, therefore on Cyrus with murder setup Thunderbird ends up showing only INBOX as available folder.
The same command works (returns list of folders) if it is run upon single Cyrus IMAP server.
The issue (Thunderbird not displaying folders) on murder setup can be solved by disabling SPECIAL-USE and CREATE-SPECIAL-USE capabilities on frontend servers.
Second issue:
Although SPECIAL-USE CREATE-SPECIAL-USE capabilities are advertised, it doesn't seem that Cyrus is supports them. Adding "xlist-*: <special-use name>" to the imapd.conf doesn't create the annotations. Adding the annotations with cyradm command "cm --specialuse \\Sent" doesn't work either. Long story short - special-use annotations are not returned.
Cyrus version: cyrus-imapd-2.5.2-3.el6.kolab_14.x86_64