NASA knew about Van Allen Belt radiation.
It is not a fatal radiation zone.
NASA shielded spacecraft and avoided the Van Allen Belt.
More
here but I'm not going to swear by it.
[quote]The Van Allen belts are full of deadly radiation, and anyone passing through them would be fried.
Needless to say this is a very simplistic statement. Yes, there is deadly radiation in the Van Allen belts, but the nature of that radiation was known to the Apollo engineers and they were able to make suitable preparations. The principle danger of the Van Allen belts is high-energy protons, which are not that difficult to shield against. And the Apollo navigators plotted a course through the thinnest parts of the belts and arranged for the spacecraft to pass through them quickly, limiting the exposure.
The Van Allen belts span only about forty degrees of earth's latitude -- twenty degrees above and below the magnetic equator. The diagrams of Apollo's translunar trajectory printed in various press releases are not entirely accurate. They tend to show only a two-dimensional version of the actual trajectory. The actual trajectory was three-dimensional. The highly technical reports of Apollo, accessible to but not generally understood by the public, give the three-dimensional details of the translunar trajectory.
Each mission flew a slightly different trajectory in order to access its landing site, but the orbital inclination of the translunar coast trajectory was always in the neighborhood of 30