You might want to study the dependencies of Firefox, and see whether there is reason to be suspicious about one of them. Or, maybe remove/purge Firefox and all of its dependencies, rename the user config files related to Firefox, and try a new installation.
If you have access to a second hardware system on the same router, it would also be interesting to know whether Firefox is a problem on that one also. Even if it were a windows system, you could boot a Linux live USB stick with Firefox on it, and test it that way.
If you are using a laptop, it might be interesting to go find an open wifi spot and try through a different router.
Just some ideas for you.