Ingesting alpha emitters is bad, but fortunately, we don't do that very often. Ingesting beta-emitters at LOW levels is something we have evolved to cope with, since even as necessary an element as potassium has naturally occurring beta-emitter isotopes.
But both beta and alpha emitters are more harmful to us once ingested or inhaled. Fortunately, in every day life, we get exposed to very little of that. Even after Fukushima and Chernobyl, most of us are more exposed to such emitters left over from atmospheric testing than from these two accidents. But even that source is swamped by naturally occurring isotopes (again, at low levels) in our food.
Now true, Cs-137 is being found in fish from the Tohoku area, but still at low levels, too low to keep me from enjoying sushi! Besides: the biological half-life of these elements (I and Cs) in the body is low enough (1-4 months) to keep it from accumulating in humans at a dangerous rate.
As for the reports of plutonium appearing after Fukushima, that was another initial, unreliable report: later reports showed that trace amount was from earlier fallout, most likely from that dark period of atmospheric nuclear bomb tests.