What is your definition of a nondeterministic system then? Typically it's a system with a non-deterministic transition relation. E.g., assuming for simplicity a system state sharded into two shards with numerical states, and the initial system state (0, 0), a non-deterministic operation can take (0, 0) to either (1, 1) or (2, 2). Then if you let each shard's replicas run independently, you could end up in an inconsistent state (either (1, 2) or (2, 1)).

So I suppose that your definition of nondeterministic must differ, but I can't figure out how.