Update Oct 12th:
It very much looks like previous installation of a custom ROM causes some sort of screen issues, but does not brick the phone completely:
This also means that if you did not install a custom ROM on your phone in the past, you should not be affected by this particular problem.
Original post and overview:
I went though all the reports here and will try to sum up the information people gave about their phone setups to get an idea what those might have in common. Thanks @USB-2 for the idea!
(click the arrow for details)
Unfortunately, not a whole lot of reports include the relevant information. So I’m tagging those here in hopes that they might still add that information:
Overview of people/phones with problems and their setups
@Tuzzaman: 
G33K2303: Divest OS according to this
M4rk: used custom ROMs (LOS), bootloader locked
@Martin_1964: open bootloader, no information on custom ROMs - please specify! according to this LOS as well
Munk: used custom ROMs, locked bootloader
GunniMator: used custom ROMs (LOS)
Devilicate: previously rooted and used custom ROMs, bootloader locked
urglas: used custom ROMs (LOS), bootloader locked
ogghi: used custom ROMs (LOS), bootloader locked
soyatti: used custom ROMs (LOS)
dylanwhyte: used custom ROMs (LOS)
Phk: used custom ROMs (LOS), bootloader open
Conclusion based on this spotty information: Most of people with the issue who reported back have installed a custom ROM at some point in the past! This would be 100% if we knew for sure what @Martin_1964 was up to. I guess you don’t unlock the bootloader just for fun. 
To be clear: I’m not convinced that this is the whole picture, as at least some of the other posts could be read in a way that suggests absolutely no modifications at any point in the past. But the only way to be sure is if those people also reported back, so please do if you can!