ok,
first to your questions:
No errors in Nginx
Yes, the token is setup.

I have further looked into this, since my live server went through a few upgrades i have made a fresh installation in a dev jail and i got the same result.
So i attempted to debug a bit and it looks to me that the issue comes from mlmmjadmin or potentially some python module.
I tried making a query with curl using this format (taken from  the readme.md):

curl -X POST \
    --header 'X-MLMMJADMIN-API-AUTH-TOKEN: 43a89b7aa34354089e629ed9f9be0b3b' \
    -d "owner=postmaster@a.io&only_subscriber_can_post=yes"
    http://127.0.0.1:7790/list@domain.com

of course i replaced the token, postmaster@a.io with an email present in the system as well as 'domain.com' with a domain present in the system (possibly replacing postmaster@a.io and domain.com was not necessary for testing purposes, but...)
the response i get is "Internal Server Error".
I added DEBUG = True to /opt/mlmmjadmin/settings.py but i get the same response...

Any additional debugging that i could run?

here is the error:

# python mlmmjadmin.py
Traceback (most recent call last):
  File "mlmmjadmin.py", line 18, in <module>
    from libs.logger import logger
  File "/opt/mlmmjadmin-1.4/libs/logger.py", line 16, in <module>
    facility=settings.SYSLOG_FACILITY)
  File "/usr/local/lib/python2.7/logging/handlers.py", line 761, in __init__
    self._connect_unixsocket(address)
  File "/usr/local/lib/python2.7/logging/handlers.py", line 804, in _connect_unixsocket
    self.socket.connect(address)
  File "/usr/local/lib/python2.7/socket.py", line 228, in meth
    return getattr(self._sock,name)(*args)
socket.error: [Errno 2] No such file or directory

It seems that it might be an error related to logging.
My rc.conf has the flowing lines:

# Prevent syslog to open sockets
syslogd_enable="YES"
syslogd_flags="-ss"

These are recommended settings for a FreeBSD jail but it might affect the logging behavior...
I can try removing those entries if you think that might be the culprit.
thanks

2 possible solutions:

1) What's the local socket file of syslog? Default is /dev/log, does FreeBSD jail have same socket? if it's different, try to add a parameter in /opt/mlmmjadmin/settings.py like this:

SYSLOG_SERVER = '/dev/path/to/log'

2) Does your jail support logging to the host syslog service? If yes, try to add 2 parameters in /opt/mlmmjadmin/settings.py like this:

SYSLOG_SERVER = '<ip>'
SYSLOG_PORT = 514

After updated settings.py, you need to restart mlmmjadmin service.

the output is:
http://127.0.0.1:7790/

Very weird.
If i submit a new mailing list with the script running from command line, it works!
But if i start it from /usr/local/etc/rc.d/mlmmjadmin start
it still gives me the error!

when used  https://docs.iredmail.org/upgrade.mlmmjadmin.html
to upgrade .

cd mlmmjadmin-1.4/tools/
bash upgrade_mlmmjadmin.sh

that is working .
Sorry my bad.