The thing is that they have been living with radiation for a very long time. Even their cars are powere dby nuclear reactors, even before the war. Power armor is a portable nuclear power core on the back, for instance. Mr. Handy is a massive nuclear reactor as well.

It's stated, for example, in Chernobyl that plants and animals can mutate to become immune to the harmful effects of radiation. In that timeline, humanity has become pretty much immune to the cancerous effects of it, but not the threats of overdose, as what happens when you reach 1000 rads.

As a general rule, people in the wasteland die before cancer would be a problem