In MySQL how do I grant a user access to a read replica only?
Master and slave instances can have different users and access permissions -replicated queries are executed by the SUPER user-, just create and/or modify the separate users with SET SESSION sql_log_bin = 0; every time (so you do not create conflicts on replication). Avoid any other process writing directly to the mysql.user (and other mysql.*) tables directly and you will be fine.

You probably want to set your slave as read_only and not provide SUPER privileges on anyone else there (as it will become out of sync if someone writes there and not to the master).