The thing is there's more than one type of radiation.
Alpha particles can be stopped by a sheet of paper for example but if you inhale radon gas those alpha particles can mess up the cells in your lungs good and proper!
Neutron radiation is nasty because they're neutrally charged and so can penetrate a lot of matter and can be big enough to do damage to what they hit - you get that in nuclear power stations.
To protect against neutron you neeed matter - lots of it densely packed, sand is good, lead is better.
At the far end of the scale a neutrino could pass through a light-year of lead without interacting with anythin - or causing any harm. - infact as you read this they are litterally flodding through your body .