Radioactivity is not anything of a new; radioactivity and its accompanying radiation (the so-called ionizing) have always existed in the Universe. Radioactive materials are part of the Earth and even human beings are slightly radioactive, because in any living tissue the smallest amounts of radioactive substances are present. There are natural sources of radiation are natural, independent of humans, and man-made sources of ionizing radiation, aimed at serving the people’s needs: scientific, industrial, transportation, chemical, medical, agricultural etc. Obviously, all activities related to the receipt and use of artificial radiation must be thoroughly controlled by special technical means.
Of course, visiting the place of a nuclear catastrophe is not a pleasure trip, and radiation safety rules cannot be ignored. Within the safety policy, the visitors are obliged to wear long clothes and closed shoes and cannot take any items found from the territory of the ChEZ: under Ukrainian law, this is equivalent to the movement of radioactive waste and is considered a criminal offense. Upon departure, everyone passes double dosimetric control, as well as the transport.
Also, according to the rules, you can’t smoke outside designated areas, sit or lie down on the ground, eat any mushrooms, fruit or berries and drink water from puddles if it suddenly crosses one's mind. The guests should strictly follow the guides' instructions. All accompanying guides undergo special training, receive a license to perform excursions to the Chernobyl Exclusion Zone and know how to avoid any danger, not only that from radiation, but also from the partly-ruined buildings and the wildlife.
So, as a matter of fact, a tour to Chernobyl Exclusion Zone, under condition of strict observance of the safety rules, may cause no more harm to your health than a flight from London to Kyiv.