I've tested this:

1) disable selinux (setenforce 0) OR enable 2004 port for cyrus: semanage port -a -t cyrus_port_t -p tcp 2004

2) service cyrus-imapd restart
3) netstat -lpn | grep 2004
cyrus is bind to port 2004

4) tcpdump -vv | grep -e mupdate -e 2004 -e 3905
> client tries to connect to mupdate port instead of port 2004

client ignores mupdate_port from config file, it even seems this was never used??? because there is only one line in the whole sources ( grep -i -r mupdate_port cyrus-imapd-2.3.7/ ): 
cyrus-imapd-2.3.14/lib/imapopts.h:  IMAPOPT_MUPDATE_PORT,
^^^ just an item in enum
cyrus-imapd-2.3.14/lib/imapopts.c:  { IMAPOPT_MUPDATE_PORT, "mupdate_port", 0, (union config_value)((long) 3905), OPT_INT, {  { NULL, IMAP_ENUM_ZERO } } },

mupdate-client.c:
backend_connect(NULL, server, &mupdate_protocol,....
-> getaddrinfo(server, mupdate_protocol->service, &hints, &res0);

where mupdate_protocol->service = "mupdate" set in mupdate-client.c


In latest sources (Fedora 11 has cyrus-imapd 2.3.14) there is no change.

this is more like feature request because it seems this was never working...

This request was evaluated by Red Hat Product Management for
inclusion, but this component is not scheduled to be updated in
the current Red Hat Enterprise Linux release. If you would like
this request to be reviewed for the next minor release, ask your
support representative to set the next rhel-x.y flag to "?".

This request was evaluated by Red Hat Product Management for
inclusion in the current release of Red Hat Enterprise Linux.
Because the affected component is not scheduled to be updated in the
current release, Red Hat is unfortunately unable to address this
request at this time. Red Hat invites you to ask your support
representative to propose this request, if appropriate and relevant,
in the next release of Red Hat Enterprise Linux.

This request was evaluated by Red Hat Product Management for
inclusion in the current release of Red Hat Enterprise Linux.
Because the affected component is not scheduled to be updated in the
current release, Red Hat is unfortunately unable to address this
request at this time. Red Hat invites you to ask your support
representative to propose this request, if appropriate and relevant,
in the next release of Red Hat Enterprise Linux.

This request was erroneously denied for the current release of
Red Hat Enterprise Linux.  The error has been fixed and this
request has been re-proposed for the current release.

This request was evaluated by Red Hat Product Management for
inclusion in the current release of Red Hat Enterprise Linux.
Because the affected component is not scheduled to be updated in the
current release, Red Hat is unfortunately unable to address this
request at this time. Red Hat invites you to ask your support
representative to propose this request, if appropriate and relevant,
in the next release of Red Hat Enterprise Linux.

This request was evaluated by Red Hat Product Management for
inclusion in the current release of Red Hat Enterprise Linux.
Because the affected component is not scheduled to be updated in the
current release, Red Hat is unfortunately unable to address this
request at this time. Red Hat invites you to ask your support
representative to propose this request, if appropriate and relevant,
in the next release of Red Hat Enterprise Linux.

Does not meet criteria for RHEL5 - phase 2 support, moving to RHEL 6.

This request was evaluated by Red Hat Product Management for
inclusion in the current release of Red Hat Enterprise Linux.
Because the affected component is not scheduled to be updated
in the current release, Red Hat is unable to address this
request at this time.

Red Hat invites you to ask your support representative to
propose this request, if appropriate, in the next release of
Red Hat Enterprise Linux.

Red Hat Enterprise Linux version 6 is entering the Production 2 phase of its lifetime and this bug doesn't meet the criteria for it, i.e. only high severity issues will be fixed. Please see https://access.redhat.com/support/policy/updates/errata/ for further information.

Moving to RHEL-7

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory, and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

https://access.redhat.com/errata/RHEA-2017:1932