Turns out you can run Firefox in Docker. It's actually pretty easy:

Code

From my github gist.

Installation instructions (on Linux):

# install docker and start the docker daemon
$ git clone https://gist.github.com/29e7e829341d58abe370.git docker-firefox
$ ln docker-firefox/ff-docker /some/path/for/binaries
$ ff-docker -b  # -b pulls & builds container, etc used for first time startup.

Notes

I attempted to use Alpine Linux as a proof-of-usability, since it's the hip new kid on the containerization block¹, but as it turns out Alpine's Firefox package is pretty fucked².

I use dmenu, this means I can run ff-docker from my desktop without opening a terminal, effectively making it a super-private-yet-convenient drop-in for Firefox. Pretty neat right?

Conclusion

This was pretty simple but effective in terms of giving me the option to have more privacy. I can see it being extended to add even more security; e.g., routing all of the traffic in the container through a VPN would be easy enough. Food for thought [citation needed].