The following is a list of all connections that Firefox may establish at application startup and how to stop them.
A loopback connection (to IP address 127.0.0.1) on non-Unix machines [1]. The browser is communicating normally with itself, and it is not recommended this be blocked.
Loading Live Bookmarks. Deleting all Live Bookmarks will stop these connections.
Checking for application updates. "Tools -> Options -> Advanced -> Update" provides options to disable update checks.
Loading home page. Setting the homepage to a blank page or a local page will stop this connection.