I'm not sure it's evolution so much as it just isn't likely to have much of an effect.
Well, actually, it is evolution, in the sense that background radiation is responsible for many of the small, meaningless mutations that add up to evolution over a very long time, but yes.
And radiation does cause damage in ways that would be quite hard to deal with, if our bodies didn't know how.
Hell, the kinds of radiation that aren't light (alpha and beta) are basically harmless in most circumstances anyway.
They cause mutations and cancer, so they're hardly harmless. Good news: they're so easily blocked, one is really only in trouble if alpha- or beta-active matter ends up inside one's body. Bad news: the air of most houses contains alpha-active Radon-222, which goes inside your lungs when you breathe. Ergo, breathing air causes cancer. The obvious solution is to stop breathing.
It's kinda both ways. Gamma radiation is dangerous, because it can only be blocked by stuff like a large lead sheet... but is the weakest in terms of destructive potential, exactly for the same reason - it goes through.
Alpha/beta are 'harmless' most of the time - because they can be stopped by, in the former's case, a sheet of paper... but that's because they are a cannonball compared to the gamma's bullet - if you remove all the pesky barriers between them and the important organs you're gonna have a *bad* time.
100% percent of people who breathe die. COINCIDENCE?
Eeexactly.