Maybe the justification for interstellar colonization will be so we can run a DM experiment on the near-relativistic ship during the trip. Boost those dark matter particles to some good fraction of c for easier detection.
I wonder what is the speed at which interstellar neutrino bombardment becomes lethal to a crew considering it’s essentially impossible to shield against them. You can put a mountain in front of the ship, but neutrinos will just pass through it like is a cloud.
OTOH if the ship is so fast neutrinos are a problem to the crew, that mountain will be suffering some intense ablation from everything including neutrinos that’ll hit it.
The real possible problem would be massive dark matter particles. These would be traveling now at around 300 km/s, so a relativistic spacecraft would boost their speeds by three orders of magnitude and their energies by six orders of magnitude or higher. And, of course, the number passing through a given area in the vehicle per unit of time would also be orders of magnitude higher. If the interaction cross section is high enough (and not so high they could be shielded) then travel at that speed becomes impossible.
The more massive DM particle issue I discussed might be problematic even with very little time dilation.
Even Alcubierre-White warp drives would create interesting problems because compressing spacetime in front of the ship would heat up whatever matter is there.
Unless something miraculous happens, I don't think we'll live to see these problems in real life, but, if we do, it'll be fun to work in solving them.
https://physics.aps.org/assets/0ce5ba95-0367-46ce-890b-de3a4...
(which is from https://physics.aps.org/articles/v14/96)
This process was first observed only fairly recently, at the Spallation Neutron Source using neutrinos from stopped pions. IIRC, they realized a service corridor under the target room would be unintentionally suitable for the experiment.