Don't worry about it, there are plenty of ways to get around the radiation. None of them are very easy or cheap (not right now anyway) but there's no reason to think it's an unsurmountable problem.
One way to get around it is to simply send your ship up into orbit in pieces in multiple launches and assemble the ship in orbit. Of course, all those launches would be ludicrously expensive. We could also just work on manufacturing materials that are lighter and more effective at blocking radiation
(like this).
And then there are the more exotic ideas involving electrostatic fields (
(Linky). Of course the downside to those are the fact that they require energy, which means it could be more cost effective to simply reinforce the hull and use your fuel for other things. It depends really on how much extra energy it costs to keep something like this running vs the added costs of launching the extra mass into orbit and then getting that extra mass to move once the ship is assembled. Even if the "shield" is more energy efficient, you could still run into some problems if the system suffers irreparable damage. Something like this would probably be a lot more fragile than a reinforced hull.
So yeah, it's a problem, but not an impossible one.