MySQL replication and master users on slave server
The "user" that the Slave connects to the Master with -- It needs only REPLICATION SLAVE, no other privileges.  Replication's goal is to keep the Slave identical to the Master.  This goal overrides any privilege issues.
The Slave should have read_only = ON as an extra protection.
"Users" (either human or application), other than the system admin, should not have SUPER privilege.  This keeps you out of trouble, and helps prevent hacking.
Another hacking prevention is to GRANT users access only to dbname.*, not *.*.  The latter would include the system tables where all the Grants are stored.
Users need write permissions when writing to the Master.  Don't worry about whether the users have write perm to the Slave; the Slave user bypasses that kind of check.  (This is probably the answer you were looking for.)
Users need only read permission when reading from the Slave.
TEMPORARY tables follow different rules.  (It is something you might want to use on a read-only Slave.)  I hesitate to spell them out here, because I am not sure of the rules.