User privileges are replicated only if the mysql database is replicated. That is, the GRANT, REVOKE, SET PASSWORD, CREATE USER, and DROP USER statements take effect on the slave only if the replication setup includes the mysql database.

If you're replicating all databases, but don't want statements that affect user privileges to be replicated, set up the slave to not replicate the mysql database, using the --replicate-wild-ignore-table=mysql.% option. The slave recognizes that issuing privilege-related SQL statements have no effect, and thus it does not execute those statements.