You can use conditions to filter the replication of that property to certain clients. The most appropriate check that exists is probably filtering to the owner.
DOREPLIFETIME_CONDITION( AActor, Property, COND_OwnerOnly ); // Send only to the owner of this actor
DOREPLIFETIME_CONDITION( AActor, Property, COND_SkipOwner ); // Send to everyone but the owner
etc.
You can check out the other conditions as well, though the rest may not be appropriate for what you want.