How to get readonly access to mysql files via g+w permission 750 or 640? The data-dir itself has permissions 700 thereby limiting access to the mysql user.

I want other folks who I add to the mysql group to be able to read binlogs and download the *.frm, *.MYI, *.MYD files to their local computer.

My first thought is to run chmod g+rx data-dir.

The database directories and table/binlog files within data-dir have permissions with 770 / 660. So I have to chmod g-w on all of those to prevent accidental tampering or removal of live data.

Unfortunately, as new binlogs are created, and the create database or create table command is used, the g+w permission is automatically added. How can I change this functionality?
Well, I found online that the environment variable UMASK and UMASK_DIR must be set, regardless of what the command umask will output.

One must add export UMASK=0640 and export UMASK=0750 to the top of their startup script, immediately before calling mysqld_safe.

The leading zero is important to switch to the octal numbering system.

The first thing I tried was 0027, but that produced files with permissions u=rw,g=w,o=rwx so that is what prompted me to invert the permissions in the environment variable to 0750 (and 0640) to produce the desired results.

I hope my self-answer will help a future visitor. :-)