Back in November I had upgraded to Big Sur (Mac OS version 11.0) from Catalina. Upon upgrading, when my Thunderbolt Display was plugged in the OS would not boot. I reported this to Apple (and here on this board). Apple ran diagnostics and told me that this was an unexpected side effect of the upgrade process (I believe a firmware modification) and that on upgrade to the next patch - they expected to have this fixed.
I checked the 11.1 release notes and it is not listed. But assuming that what the development team told me - this is not unexpected. As it was a pretty widely reported but non-critical issue (which is why they did not expect to release a special patch just for the monitor issue).
Last night I upgraded to Big Sur 11.1 - and the issue is now fixed! Here is what I did ...
First I started the upgrade with everything plugged in (that means the Thunderbolt Display and my other peripherals - which attach thru it and my other thunderbolt hub, a Legato port replicator). After the first boot - the machine hung up just like it has before whenever the Thunderbolt display was plugged in. I expected this to happen because the first boot is really nothing but a reboot after the download to initiate the upgrade.
So after I manually hard powered down the MacBook Pro by holding the power button - I restarted the boot process. Upon seeing the first Apple symbol on the screen (now of the MacBook's built-in display) I plugged the Thunderbolt Display into the machine.
The upgraded proceeded as normal. It rebooted several times, I want to add, without issue. The process ended late in the evening and I came back to the machine this morning. I reconfigured all the physical connections by removing everything from all the ports, booting the machine without any displays (I also have an HDMI display attached) and any other peripherals. Then rebooted. And finally put everything back together again ... and did one final reboot.
As of right now ... everything is working and the machine appears to boot correctly.
I believe, that the upgrade migrated the firmware back to a point where the Thunderbolt Display can now be booted. And that by plugging the monitor in at the beginning of the upgrade process the upgrade did that. My guess is that anyone that has downgraded back to Catalina, might be able to fix their boot up issues with the display by also upgrading to Big Sur 11. If they want to remain at Catalina; they could downgrade again -- that though would be a pretty painful process as it would like take 3-4 hours running a 6+ year old MacBook like mine.
Good luck to everyone ... it sounds like Apple has done what they said they would do. If you still cannot get your display to boot up properly I would suggest contacting Apple Support and having them analyze your specific issue. It might be something different than what I and some others have reported.