Have cosmic rays and the CMB affected Earth's history? Do cosmic rays and the cosmic microwave background carry with them enough energy to have a macroscopic effect on events on Earth?
The most obvious example I can think of is by giving animals cancer. Maybe you can think of others. If they don't have a direct effect, maybe they can affect events indirectly via our Sun or upper atmosphere (butterfly effect)?
Therefore, if the stars were in different places or supernovae occurred at different times, would the history of life on Earth be completely different?
 A: There is an intriguing possibility that the answer is yes, in a very fundamental way!
All amino acids (except glycine) come in two chiralities, left-handed and right-handed, related by parity. However, all amino acids used in living beings are left-handed. Evidently, by chance, early in Earth's history, left-handed compounds gained an advantage somehow. Then this imbalance just grew, until they completely dominated right-handed compounds.
There are several competing theories on the origin of this imbalance. One proposed explanation was the weak force, which breaks parity symmetry, but its effect is tiny. A more recent hypothesis is that circularly polarized light from nearby nebula, which hit the early solar system, preferentially destroyed right-handed compounds and created the original imbalance. Thus, radiation from space may be responsible for the chirality of life on Earth.
This is a research topic, so nobody knows for sure if the hypothesis is true. If you want to read papers on it, the keyword is 'homochirality problem'.
