How can I suppress "CSS file not found" errors on production? "One or more CSS files were not found or does not exist" errors are being displayed to users on production.  Of course I should fix the source of these errors, but in the meantime, I would like to suppress this error message.

On admin/config/development/logging, I have set Error messages to display to None.  Is there some other step I need to take to suppress these errors?

I have also cleared all caches (Drupal, Redis, Varnish) but the error (only present on some pages) is still being displayed to authenticated (non-admin) users.
I would first ask, are you logged in as super admin? I believe if you are logged in as super admin the message will display regardless of the setting in development/logging.

If you are not logged in as admin and are viewing the page anonymously did you clear your browser cache. If the messages are still being displayed, is your site being cached via varnish? You may need to clear the varnish cache or simply add an extra query parameter to the end of the url to make certain you are viewing an unvarnished page. Ex: www.example.com/homepage?extraquery 

This is generally unadvisable but when push comes to shove and you need to hide something quickly on the production site, you can alway hide the error message box with css until you actually fix the error. AGAIN, i would only use this as a last resort and if deadlines are rapidly approaching and there just is no other option.

You could do something like .error {display:none;} in your global.css file or wherever seems more suitable. 

Good luck