You don't have to turn tracking protection off globally. You can leave it enabled in "strict" mode, and add the x.com domain as an exception (click the Manage Exceptions... button above the mode selection).
If you also use Privacy Badger, you'll have to center the slider for twitter.com when on the x.com login page.
You may not be happy with these compromises, but the above steps are tested and working for me. I have my primary Firefox profile set to delete all cookies on close but I do not log in to Twitter using that profile. I use Twitter in a second Firefox profile which keeps twitter.com/x.com cookies on close. If I want to open a third-party link someone tweeted, I just click and drag it from the Twitter profile window to my primary Firefox instance window. This is good enough privacy for me.
To make using multiple profiles at the same time easier, create custom desktop launchers for secondary profiles and give them a different theme. This is simple on GNOME and most likely possible on other desktop environments and OSs as well.
If you also use Privacy Badger, you'll have to center the slider for twitter.com when on the x.com login page.
You may not be happy with these compromises, but the above steps are tested and working for me. I have my primary Firefox profile set to delete all cookies on close but I do not log in to Twitter using that profile. I use Twitter in a second Firefox profile which keeps twitter.com/x.com cookies on close. If I want to open a third-party link someone tweeted, I just click and drag it from the Twitter profile window to my primary Firefox instance window. This is good enough privacy for me.
To make using multiple profiles at the same time easier, create custom desktop launchers for secondary profiles and give them a different theme. This is simple on GNOME and most likely possible on other desktop environments and OSs as well.