It is only instruments like Geiger counters which can do this and no-one carries Geiger counters around with them. So we're suspicious of anything which we know contains radioactivity - like nuclear power stations. You expect it to glow blue or something, but it just lies there looking boring and grey. Not a hint that if you were to pick it up in your hand for a second or two, you'd get a lethal radiation dose which would kill you in hours. Scary, as I said.
Risk Being alive is a risk.
But our perception of what is risky is, to say the least, quirky. The nuclear industry claims that the risk from nuclear power is vanishingly small. Few have actually died in radiation accidents though, particularly after Chernobyl, thousands of lives may be cut short by the radiation spewed out by the stricken reactor. People are generally more scared of flying than driving though the air-death toll is never higher than a few hundred in any one year. There is no shortage of examples of how illogical we are about danger and risk.