This issue is not solved for me, running thunderbird's latest version on Sid's repository.
I run an XFCE DE with no Display Manager. I login in a tty, and then startx. Maybe it has something to do with that. As for the other binaries suggested to run here, I have no different results. And line "deny @{HOME}/.* r" is not present in /usr/bin/thunderbird. Terminal output when running thunderbird is: No protocol specified Unable to init server: Could not connect: Connection refused Error: cannot open display: :0.0