Radiation exposure will be easily survivable in the short term. Astronauts have already lived in space for longer than a Mars flight, and Mars explorers will have, at a minimum, highly shielded sleep areas during the trip. With a VR setup, spending a lot of time there might not be too bad...

Spaceflight oriented radiation shielding will also improve over time.

On Mars, radiation won't be much of a concern at all, since all living quarters will be underground, either under piled regolith, or deeper underground.