Neutrons - This is only a hazard in the immediate vicinity of a nuclear power plant or a nuclear blast. All nuclear power plants are well shielded against the release of neutrons so this is not regarded as an important problem. Fuel rods do not emit neutrons in any meaningful amounts. Betas - Beta rays are simply high energy electrons. They travel at most a couple of feet in air and can be shielded by clothing or skin.
Betas are only a hazard if the radioactive atom is inside the body.
Either inhalation or ingestion will bring the radioactive atom in contact with living tissue in the intestines or lungs. Should a radioactive atom such as Sr-90 pass through the intestines it will be absorbed by the body. The body thinks of most metals as being like calcium and deposits them in the bones. This isn't good as that puts the radioactive metals in the immediate vicinity of the bone marrow where red and white blood cells are being produced. When the atom decays, the full energy of the beta may be deposited in the tissue.