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BrowserMatch "^Mozilla$" I believe should work but I wanted to get a second opinion before I update my live server which has dozens of unique visitors every minute. Don't want to accidentally ban all Mozilla UAs
That user-agent regex looks good to me, but since you're using mod_setenvif to set a variable for later use by mod_access, also make darn sure you check your Order and Deny from directives against the documentation, too!
BrowserMatch "^Mozilla$" Getout
Deny from env=Getout
Allow from all