Firefox is available as a bare-bones browser which you can enhance with third party Add-ons from the Mozilla Add-ons site.

Messageware however doesn't appear to be available as a download, so you'll need to contact the developer for support: http://www.messageware.com/

Thanks, The messageware website asks for my user account. I never signed up, never downloaded the add-on, and never agreed to have it. In Firefox, under add-ons, messageware is not listed. How do I disable the thing?

Where are you seeing this message exactly? When you visit the site, or as soon as you start Firefox?

The messageware pops up as a separate box. When closed, it pops up again and stops whatever I'm currently doing. Messageware box pops up only when the Mozilla thunderbird is open.

Is the popup blocker enabled in the content menu? See: Content Panel

If it is, install this add-on which should prevent it occurring again: https://addons.mozilla.org/en-US/firefox/addon/adblock-plus/

During the installation, you'll see the opportunity to subscribe to "Easylist" which filters out around 11,000 ads. Click OK to that one, then go to: https://adblockplus.org/en/subscriptions and scroll down to the bottom of the page. In the Miscellaneous section, subscribe to "Malware Domains" which will filter those out as well.