Getting there faster is one of the best ways to reduce the amount of radiation absorbed. Nuclear power is needed for faster rockets and powerful magnets; safe and reliable access to LEO is the first step to getting reactors in space.
Mars has no magnetosphere.
Estimates are that people exploring Mars will have to spend 20 hours a day under 10+ meters of rock to protect from solar radiation alone. I don't believe this protects from the GCR.
Much of that time in the cave will be spent on the conical treadmill to make up for the .3g low gravity. The impact on human biology over longer term is unknown.
I think for actual work, living and use space is almost uninhabitable without the active shielding problem being solved. Risking cancer for a select few isn't the issue, its making space a place humans can live.
However with active shielding, approaches like L5 colonies and in deep space become viable. They could be made far more human habitable then any of the planets or moons.