The claims a home should care about is: what is the plant as a unit exposing it's external environment to? Nothing else pertaining to radioactivity matters. The waste at a coal plant is spewed into the external environment. The waste at a nuclear plant is encased in layers of lead, glass, and concrete. There is no rational way you can claim that a coal plant exposes the surrounding environment to more radioactive isotope than a nuke.
Exactly. Think of the powerplant as a black box. What threats does it expose?