why are people afraid of "radiation"?

Actually it can be bad in low doses too. It depends on the type of radiation, and the effects build up over time.

As you say, some is non-ionising. Light, radio, TV, they're all electromagnetic radiation and of course those do nothing to you at all. Except if it's at the right microwave frequency to cook you. Or it's at such a high frequency that it causes ionisation - X-rays and gamma rays - or it burns, like the Sun's UV that can give you sunburn... er, not so simple, is it?

But people who don't know that much about physics just see the word "radiation" and don't know, or forget, it's not all the same. What they DO know and understand is history, and they've probably heard of Hiroshima and Nagasaki. Or Chernobyl - I'm old enough to remember when the nuclear power station there overheated and went into meltdown. (It was about the time I finished my physics degree!) Or Three Mile Island. So "atomic" and "nuclear" are bad words too.

If only we could put the jack back into the box and insist that the ionising stuff is "radioactivity". But life doesn't pan out like that... when radioactivity was first discovered, it looked like some new kind of rays, so the scientific papers called it that and... oh well, it's done now. And it IS radiation too, because it radiates through space, right?

Except when it's not... alpha and beta radioactivity aren't really radiation, they're particles thrown out from radioactively decaying atoms, but of course nobody knew that to start with. Not particularly dangerous either - an effective shield against alpha particles is a piece of paper! An inch of wood will do it for betas. It's the gammas that gonna git ya, boy...

So much for the science, but we're stuck with the English language and the way people respond to certain words from what they've heard before. Mostly it works. I say "cat" and that conjures up a picture in your mind. You might not be thinking of the same breed as me, but a cat's a cat - small furry creature that goes "meow". If you say "dog", I know what'll come up first for me - my sister and her partner have a beagle. Big ears, brown, black and white, will rip up anything and the only way to get any peace when he wants to play is to play with him until he gets tired. But what does "radiation" conjure up? For the general public, something about atomic bombs and nuclear accidents might well be in there somewhere.

"The only time radiation is bad is in high doses. "

You're absolutely incorrect. Low dosages of radiation over long periods of time can be just as lethal as high doses over as short period of time.