Firebug should be deactivated by default so, if you don't open it for
mail.google.com it should stay disabled.
If you use "On for All Web pages" option (in Firebug's
status bar menu) - which causes Firebug to be enabled by default - you
can disable Firebug specifically for
mail.google.com by pressing
"Deactivate Firebug for this web site" button (The red one of the far
right side of the Firebug's tab-bar). In this case the URL will be
black listed and Firebug is disabled if it's loaded again.
For more details, see also:
http://www.softwareishard.com/blog/firebug/how-to-enable-and-disable-firebug-15/
Honza