As Nick rightly says, there is no rig that is bream proof.
That said, I can honestly say that I've never caught a bream on a chod rig, tench yes but not bream. Obviously not saying you won't catch bream on them but for some reason I never did and I used them a lot and on waters that held large shoals of big bream .
Also as has been said above, what you feed and how will determine if bream become a pain. I know a few angler's that only use 22mm / 24mm baits and hardly if ever get bream problems.