Well, technically isn't sunlight radiation?
Many English words have several related but distinct meanings. "Radiation" in the context of nuclear physics refers to the various ways in which an atomic nucleus can disintegrate, and the resulting EM emanations and kinetic particles.
Sunlight could even be construed to fit this definition, considering it's origin, but in general, no, sunlight isn't radiation one would expect to sample from nuclear reactions.
As far as "is nuclear power safe" - no, it's not. But neither is coal mining or off-shore drilling.
It's the potential mutations from radiation that creep me out - and not from a totally rational point of view, just the horror factor.
Germ cell mutations caused by radiation are by far the smallest effect that can occur from exposure to radiation. Consider the chances:
1. The radiation must ionize the right part of the cell, the nuclear DNA. The DNA in a cell is a very small amount of the contents of the cell; it resides only in the cell's nucleus, and it has to affect one or more base pairs; a hit on a ribose component probably won't do it.
2. It has to hit the DNA in such a way that one or more base pairs are altered or deleted, without causing damage extensive enough to kill the cell outright. There is a very small window of opportunity here: it has to cause a visible change in the physiology of the resulting fetus, but not one which will debilitate to the point of immediate death. This is, statistically, a perhaps one in a thousand shot.
3. Consider that the normal germ cell houses 150 mutations unique to itself from its original parental DNA. This adds one more to the mix. It is this reason which negates most claims that a particular defect in a particular baby was caused by radiation; it is simply impossible to know, except statistically.
4. The cell has to be a germ cell, an egg or sperm. If it isn't the mutation will not be heritable by future generations. (Mutations to other cells are known as somatic, and are more usual as non-heritable cancers.)
5. The mutation must evade the cell's normal methods to repairing DNA errors.