The first time audiences see this aspect is when Lyudmilla goes to the hospital to see her very sick husband, Pripyat firefighter Vasily Ignatenko, who is dying from severe radiation sickness.
The nurses and doctors are adamant about her not seeing her husband for fear that she could be affected by the radiation.
People with radiation sickness are quarantined to protect the sick themselves, due to their severely weakened immune system, not to protect those that are not poisoned by the radiation.
In reality, once all the radioactive clothing he was wearing was removed and his skin was washed, there is no serious radiation threat to those around them.