Except for the hypothesis that nucleons (neutrons and protons) break down given sufficient gazillions of years to do so, no, everything is not radioactive. True, every element has radioactive isotopes, but most elements as they occur in nature do not – their radioactive isotopes are too short-lived to have survived. Only carbon-14 and tritium, formed in the upper atmosphere by the impact of cosmic radiation on CO[sub]2[/sub] and water vapor, plus the intermediate steps in the breakdown chains of the metastable nuclides, are common short-lived nuclides.
Among relatively common elements other than carbon and hydrogen, only potassium-40 and rubidium-87 are reasonably metastable isotopes. There may be trace amounts of other radioactive nuclides in the common elements lower on the periodic table, but the operative phrase there is “trace amounts.”
Indium is an interesting exception to this rule, but the story here is interesting. Indium is present in two isotopes, -115 and -117. One is completely stable and comprises 4% pf present indium deposits; the other isotope (96% of the whole) is metastable, radioactive but with a half-life 50,000 times the age of the Universe, and thus barely noticeable as radioactive.
Every nucllide more massive than Lead-207 is radioactive, but descends from one of three metastable nuclides: Thorium-232, Uranium-235, and Uranium-238. (Bismuth-209 and Lead-208 are also metastable, to the point they were until recently considered non-radioactive, completely stable.) Of those three metastable isotopes, U-238 has a half-life just about the present age of the Earth (50% of the original amount left),Th-232 has a half-life of about 10 billion years (75-80% left), and U-235 has a half-life of just under a billion years, meaning only about 4% of the original amount is left. The various isotopes between U-238 and lead occur in relatively small amounts, as their natural (rapid) breakdown is counterbalanced by their slow, steady production by breakdown of the metastable elements. Also small traces of Np-239 and Pu-239 are present from the beta-decay of U-239 when U-238 is impacted by a neutron and does not break down in consequence – a rare but extant phenomenon.
Traces of the metastable isotopes, however, are present in the environment, e.g., in granite and in soils resulting from its breakdown (and the bricks made from them). This is why radon detection is so important in well-insulated areas.