For a relativistic rocket, isn't blue shifted background radiation the greatest problem?

If a spaceship were to accelerate at a constant 1g it could reach the other side of the galaxy (100,000 light years away) in less than 25 years, decelerating at the mid-way point so its crew could set foot on a likely planet. The crew would travel in the comfort of earth-like gravity, and the relativistic shortening of the distance travelled would make the journey easily accomplished in their lifetime. Of the remaining problems there is of course identifying a suitable planet so far away, and inventing a suitable thrust engine to produce 1g acceleration for a very mive spaceship over a 25 years period. Isn't the biggest problem of all though, the fact that the background radiation would be blue shifted well into the gamma frequency range and therefore be extremely hazardous to life?