Thunerbird then exits.If you see this message something went wrong while
migrating your Icedove profile(s) into the Thunderbird
The following error occured:
An existing profile folder (or symlink) '.thunderbird' and a folder
(or symlink) '.icedove' was found in your home directory '/home/jesse/'
while trying to migrate the Icedove profile(s) folder.
This can be caused by an old, currently unused profile folder or you might
be using Thunderbird as provided by upstream Mozilla.
If you don't need this old profile folder, you can remove or backup
it and start Thunderbird again.
Sorry, but please investigate the situation yourself.
I have never used Icedove so this message makes little sense. There is a .thunderbird folder in my home directory, but it has always been there and it contains all my e-mails/accounts. It looks like something in the update process created a .icedove folder in my home directory, but the .icedove folder is entirely empty. Deleting the empty .icedove folder fixes the issue and allows Thunderbird to load.
Hopefully this will be useful for anyone else running into this error.
Update: Since the update to Thunderbird I have also discovered that Thunderbird can no longer open URLs from e-mail messages. Clicking on a link simply does nothing, where it used to open a browser to display the linked content. When running Thudnerbird from a terminal, the application reports "permission denied" errors whenever it tries to run/open a web browser. Prior to the upgrade links opened, whether a web browser was already running or not.
I fixed this by rolling back to the previous version of Thunderbird. Specifically, I uninstalled the "thunderbird_2%3a52.8.0-1~mx17+3_amd64.deb" package, which was installed on June 7, 2018. And I replaced it with package "thunderbird_2%3a52.8.0~mozillabinaries-1mx17+1_amd64.deb" which was installed May 20, 2018.
These two packages look to be providing the same version of the e-mail client, but from different sources(?) The Mozilla package works with no problems and I can open URLs again.