Macbook Pro 2016, shuts down when moved
It turned out to be a hardware issue. One of the connectors was loose. It’s the  rossmann group details what exactly happens: briefly it’s the connector near the hinge of the laptop that causes a BSOD, by (I think) sending the LCD power rail straight to the CPU and tripping the protection features. I strongly advise anyone with this issue to promptly fix it, possibly by sending it for service (they won’t replace the LB, just the cable and that’s reasonably priced).
After fixing - no issues whatsoever.