Is there a way to have the master process log to STDOUT STDERR instead of to a file?
It seems that you can only pass a filepath to the access_log directive:
When running Nginx in a Docker container, be aware that a volume mounted over the log dir defeats the purpose of creating a softlink between the log files and stdout/stderr in your Dockerfile, as described in @Boeboe 's answer.
In that case you can either create the softlink in your entrypoint (executed after volumes are mounted) or not use a volume at all (e.g. when logs are already collected by a central logging system).