I believe that the colonization of the moon and other planets is inevitable.
And it will be people like Musk rather than government agencies that will make it happen.
Radiation away from Earth is indeed a major concern, both the slow accumulation over time or - and the Apollo astronauts were fortunate that no event occurred - quickly via a burst from the Sun.
Moon habitats will be attempted to be shielded with regolith and water barriers but it will be an in-progress monitoring exercise as they go along to find the safety margin for Moon/Mars inhabitants.