This article studies the synchronization power of AllowList and DenyList objects under the lens provided by Herlihy’s consensus hierarchy. It specifies AllowList and DenyList as distributed objects and shows that, while they can both be seen as specializations of a more general object type, they inherently have different synchronization power. While the AllowList object does not require synchronization between participating processes, a DenyList object requires processes to reach consensus on a specific set of processes. These results are then applied to a more global analysis of anonymity-preserving systems that use AllowList and DenyList objects. First, a blind-signature-based e-voting is presented. Second, DenyList and AllowList objects are used to determine the consensus number of a specific decentralized key management system. Third, an anonymous money transfer algorithm using the association of AllowList and DenyList objects is presented. Finally, this analysis is used to study the properties of these application, and to highlight efficiency gains that they can achieve in message passing environment.