User blog comment:Le Rottweiler/Radioactive Containers/@comment-1496755-20150802110749

Like Death said - explosive barrels were present in Doom, which might have prompted id to include them in Quake as well. Quake 2, Return to Castle Wolfenstein, Doom 3, and Quake 4 feature exploding barrels as well. Heretic has explosive pods, which serve the same function. Hexen II has some exploding barrels too, but they are pretty rare.

From an in-universe point of view, these radioactive containers might have been in transit to a safe disposal area, yet the invasion put a stop to this and thus they were left lying around (despite the danger of explosions and deaths).