You may say "I've heard that some radiation will be around for thousands and even hundreds of thousands of years". Yes, but those isotopes are our friends. (That may be putting it a bit strongly.) Anyway, they are not near so harmful as many people think. There is the point of view that no radiation is good for you. Some dermatologists maintain that you should not even get a suntan. (Yes, that is radiation that you get from the sun.)
There is even the theory that it is cosmic radiation that causes both overall genetic change, aging, and death. In any case we are all subjected to many sources of radiation every day. The question is not whether or not you are going to receive radiation, but how much and how quickly. Let us compare the radiation we are concerned about with another type of radiation. Heat.
Just as we measure radioactivity in roentgens we measure heat in calories. If I were to tell you that that pipe over there was going to put off a million calories of heat, you might say, "Let me get away from it!". But, if I then said that it was going to be over the next million years, at the rate of one calorie per year, you would realize that you were in greater danger of freezing to death than of burning to death if you were depending upon that pipe for heat.
It is not how much heat is going to be given off (it may be a large amount) but how much over what period of time. A mere two hundred calories suddenly inflicted upon one point of the skin would create a bit of a sting, but hundreds of thousands might be comfortably absorbed from a heating pad over an appropriate period of time.
It is the same with radiation. Most isotopes give off their energy so rapidly that they are like flash bulbs. Flash and they are gone. It just happens right in the vicinity of the bomb. Others are like regular light bulbs that give off their light and heat for some period of time before they burn out. They may travel a long way from the bomb as fallout before they dissipate their energy. For these we need a shelter to protect us if we are in their vicinity. Nothing else will do.
Still others are like those small luminescent lights that some people put in their bathrooms for night-lights. Only weaker still. They just sit there and barely glow for a very long period of time.
Little miniature flashlight bulbs or matches are a good analogy to fallout particles. One or two of them in a room with you will not harm you. But surely you can imagine the situation where if you had thousands and thousands the light would either be blinding or the heat so intense that you would be incinerated.
Fallout is just the same way. A few pieces inside a shelter with you will not harm you, but if you go outside where there are millions of the little beasts lying around then you have had it. The only difference between their radiation and the radiation from a little flashlight bulb or a match is that it is invisible radiation that you cannot see or feel - like that from an x-ray machine.