Is there a slave configuration that stops replication of mysql.mysql and grants? I have a mariadb slave that cannot have the same permissions and users as the the mysql master. Is there a way to configure the slave so that it does not replicate changes to the mysql system tables and does not try to run GRANT statements?

I am currently using replicate_wild_do_table=mydb.%, and I tried using replicate_wild_ignore_table=mysql.% but that did not seem to ignore the GRANT statements.

I noticed replicate_wild_do_table=mydb.% seems to be sufficient on a mysql slave to not replicate changes to the mysql system table, but it is not sufficient on a mariadb slave.
Use binlog-ignore-db instead. This post explains the behaviour and answers your question. If not, comment.