When mongod starts it creates the mongod.log. This initial file will be created based on the umask of the process.
However, log rotation will default to mode 600 unless honorSystemUmask is set. This behavior seems inconsistent.
This behavior appears to have been introduced with
SERVER-11887 Default file permissions on mongod and audit logs
- is related to
SERVER-37151 Allow logs to be created with different permissions than data files