Lab safety wasn't thing and the people in the lab resisted any attempt to create it. It's no surprise people died.
I’m currently reading Command and Control which dives into nuclear safety and more interestingly, accidents. I recommend it: https://books.google.com/books/about/Command_and_Control.htm...
If you believed in earnest (as they did) that the atomic bombs stood a very good chance of shortening WWII, there was absolutely no case for safety regulations short of preventing accidents that wiped out large numbers of lab personnel. Even a single day's delay would kill over a thousand times as many people as lives you'd save.
The Americans knew that the Nazis were working on atomic weapons and believed (entirely reasonably, but incorrectly) that the Nazis were likely ahead of them. What was the safety risk of a nuclear-armed Adolf Hitler?
We might as well criticize the lack of "safety culture" on D-Day or at the Battle of Stalingrad. These were people doing desperate, daring things in dangerous times at an intentionally breakneck pace.
Slotkin's accident occurred in 1946 after the war ended, so Germany was not a looming threat at that instant. But we had similar concerns about the USSR's nuclear weapons program at that time.
"Workplace safety" is a comparatively modern invention.