One of the fundamental normative principles in social choice theory is that of neutrality. In the context of judgment aggregation, neutrality is encoded in the form of an axiom expressing that, when two possible judgments enjoy the same support amongst the individuals, then either both or neither of them should be accepted. This is a reasonable requirement in many scenarios. However, we argue that for scenarios in which individuals are asked to pass judgment on very diverse kinds of propositions, a notion of relative acceptability is better suited. We capture this notion by a new axiom that hinges on a binary "acceptability" relation A between propositions: if a given coalition accepting a proposition p entails the collective acceptance of p, then the same should be true for every other proposition q related to p via A. Intuitively, p Aq means that p is at least as acceptable as q. Classical neutrality is then a special case where all propositions are equally acceptable. We show that our new axiom allows us to circumvent a classical impossibility theorem in judgment aggregation for certain scenarios of practical interest. Also, we offer a precise characterisation of all scenarios that are safe, in the sense that any aggregation rule respecting the relative acceptability between propositions will always return logically consistent outcomes.