Firefox has been hardened both security and privacy wise thanks to arkenfox/user.js.
Its configuration is being updated automatically every time you start Firefox thanks to this wrapper script.
If you're not happy with its current behavior, edit the Configuration overrides which are available in my dotfiles repo there.
As always, a line has to be drawn between security and usability. If you want a truly privacy respecting browser, use the TOR browser.
Perform CTRL + i on the website you want to stay logged into after a restart of Firefox.
Then look for "Set cookies" and untick "Use Default". Make sure the radio button is set to "Allow".