I was hoping mozilla would have their users' back, but a default install of Firefox also makes multiple connections to mozilla, google and other domains when started.
Firefox checks for updates, and will update the malware/phishing databases a bit after startup. That's actually the same SafeBrowsing the OP mentions. All of this can be toggled. I'm not sure what your vague "other domains" is.
I'm a bit puzzled at the extreme shortsightedness of a browser checking for security updates being branded as "not having their users' back".