There's a current disagreement about radiation dosing policy right now, too. One side things the current approach is fine, the other believes that we are so overly conservative that we are wasting a lot of resources avoiding doses that are inconsequential. This is most relevant if we want to build and operate more nuclear reactors (e.g. for power), but it might also change some x-ray practices.
But, there are few things that are absolutely safe. You can slip, fall, and die in the shower; you can "poison" yourself by drinking too much water. When a medical professional requests an x-ray, they believe the risk is worth the reward.