As I understand it, the basic motivation behind ruling out a naked singularity is that we don't know what is happening at a singularity and thus, we won't be able to predict anything in the universe if there is no horizon around such an unknown region. But the reason we don't understand what is happening at the singularity is that we don't have a theory of quantum gravity. But when we have a theory of quantum gravity, this limitation should go away. And thus, causality should be preserved even with naked singularities.
It is a very cultural fact that we don't know how to deal with singularities without horizons at this stage. Thus, it seems quite naive to assume that causality would actually be violated if horizons don't cover the singularity. Though, I believe under some restricted energy conditions the censorship conjecture has been proven and thus, the censorship might be correct due to some other than causality reasons but causality doesn't seem to force the censorship.