Multi-domain federations support shared network services. Many orchestrators manage the service's lifecycle. For the shared VNF Forwarding Graph (VNF-FG) reconfiguration, orchestrators update the graph's logical information, ensuring a consistent behavior for replicas. Only one work in the literature considers sharing the VNF-FG. However, it offers weak consistency guarantees, without considering the VNF-FG's nonfunctional dependencies. In case of a conflict, while updating the VNF-FG, the orchestrators solve consensus. However, this adds latency, undermining the goal of Network Function Virtualization. This paper introduces the first coordination-free multi-domain orchestration algorithm for consistent shared VNF-FG reconfiguration. Unlike the current state of the art, the proposed algorithm skips the coordination phase, offers strong eventual consistency, and supports non-functional dependencies. We present two variants: the preventive, where transient inconsistent states are prevented; the corrective, where intermediary inconsistent states, during the updating process, are tolerated. We prove the correctness of our algorithm and evaluate it. The variants, unlike the state of the art, reconfigure consistently the shared VNF-FGs without solving consensus. They offer stronger guarantees compared to the literature, like allowing orchestrators to reject ongoing reconfigurations without a high impact on performance.