Doesn't seem bad to me now, having once been a (part time) soldier and now being a classified radiation worker. Lots of machine gun and small-arms fire followed up by unfriendly locals with sharp pointy things on the end of their weapons are far more likely to kill me now than cancer is in 20 or 30 years time.The idea of them dropping the bomb on an enemy formation just before sending in the infantry seems terrible today but at the time, ignorance is bliss until you start having the VA make a lot of payments to cancer doctors a few years or decades down the line
Remember also that they were considering the massive use of mustard gas as well in conjunction with nuclear weapons. The protective equipment you need against both is actually remarkably similar.