Your python app must be writing it's output to the STDERR output channel instead of the normal STDOUT. Using the shell construct
> only catches and redirects data written to the output channel, but there are actually several other channels that can be printed to, the most common being the second one, usually used for errors.
You can try trapping STDERR (2nd channel) as well like this:
python ./manage.py dumpdata partyapp.InvitationTemplate > partyapp_dump.json 2>&1
2>&1 construct connects the output stream for errors to normal output channel. It is unusual for a program to generate output that you would want to capture on the error channel; usually that would be reserved for debug information not application data. Please use this script with some caution since it is behaving in a non-standard way.
You could also dump the output and error channels to different files like this:
python ./manage.py dumpdata partyapp.InvitationTemplate > partyapp_dump.json 2> error_output.txt