I run firefox on Debian. I made a clean install with no cookies, or no information input from my side. I've also disabled all mumboo-jumboo healthy and crash report tracking. I've disabled 'shared additional data' too.
At this time, there is no TCP connection to any website, then I leave firefox open at the 'create new tab'. When I turn off firefox, there are no packets too. When I turn it on, I see random TCP packets to websites I've visited (days ago) like 'duckduckgo' and 'cloudflare'. (I suspect they are HTTPS, since they are sent over TLS to port 443 of the respected servers).
Why? (The issue is also visible on Chromium)
Best Answer
I found the solution in a blogpost. Hopefully it helps someone.
Basically Firefox performs a number of prefetches against CDN networks (cloudflare and other), contacts google for a malware updates and contacts it's own services for addon blocklists and other security updates. These settings can all be disabled at about:config.
I tested the browser for an hour with these settings, and no side service was contacted, that I didn't expect.
Source: http://kb.mozillazine.org/Connections_established_on_startup_-_Firefox