First,due to a shortage of credentialled teachers, hundreds of teachers in California are teaching with emergency credentials. That is, they have passed a test (the California Basic Educational Skills Test CBEST) but do not have a teaching credential.
So apparently you can teach in the California public schools without being properly credentialed, but you can't homeschool.
Read Lois Kazakoff: Should homeschool teachers have credentials? and feel free to leave a comment.