I can accept that reality talks to itself faster than light, though it is moderately troubling if we haven't found a covariant way to describe such a situation of real things we are uncertain about.
Robin, can you clarify the second half of this sentence? Are you troubled that there is no local realistic model for the predictions of quantum theory, or by something more subtle?
Are mixed states really the main battlefield? It seems to me that the subjective vs. objective debate for mixed states is not much different from the classical case, except it's much messier mathematically, just as Eliezer writes.
Rather, the interesting question for me (and, as I understand, the quantum Bayesian crowd) is whether pure quantum states should also be interpreted as states of knowledge.