disable addons
There are a few addons installed on Ubuntu by default installation.
- EDS Contacts Integration for Thunderbird
- Global Menu Bar integration
- Messaging Menu and Unity Launcher integration
Some of them might be risky.
For example "Messaging Menu and Unity Launcher integration" syncs with the Evolution Data Server (EDS). And the EDS possibly syncs with Google and/or Ubuntu One. (source of that information)
Contacts from Thunderbird/TorBirdy should not be uploaded and stored unencrypted in any cloud.
My suggestions is, do it like TorButton, deactivate most addons. Perhaps with the exception of enigmail (#6019 (closed)) and mixgui (#6020 (closed)). Allow users to override the function, at least through an about:config setting.
To upload designs, you'll need to enable LFS and have an admin enable hashed storage. More information