In 1969 we "Landed on the moon" but how can we get past these huge radiated "doughnut" shaped belts Is a mystery to me
The Astronauts were exposed to the radiation not only as a consequence of passing through the Van Allen Belt but also being exposed to the radiation from the Sun.
The amount of radiation would have certainly been lethal had they spent more time in space than they did.
But for the up to eight days the Astronauts spent out of the protective cocoon of Earth's natural radiation shield the astronauts were not in any real danger.
On the other hand, the danger of a sudden major solar flare-up resulting in radiation exposure so intense to have killed the astronauts in space was always a possibility.