charged particle radiation is not hard to sheild for. betas, the most penetrating, only need a few cm of relatively dense material. heavy ions are stopped by a sheet of paper.
Only if those ions etc. have a relatively low energy level. If you are referring to the alpha and beta particles kicked off by radioactive decay, then typical kinetic energy is only going to be on the order of 5 MeV or less most of the time. The minimal shielding you describe would be adequate.
However, a significant portion of the charged particle radiation in space is cracking along at relativistic and ultrarelativistic velocities. I'm seeing 40 MeV being quoted by Wikipedia as a threshold beyond which damage is likely to occur. The Sun can whip out particles with KE in the GeV range. Galactic cosmic rays have been observed with energies of as much as 10
20eV. And the real kicker is that unless your shield is a veritable sponge for low AND high energy radiation, the thicker it is, the more secondary radiation you are going to create from spallation.
I do not think it is an unsolvable problem, but it is not a trivial one. Many solutions have been considered. The ones that are most likely to be effective are some of the most difficult to implement because of our extremely limited surface-to-orbit lifting capacity.