Can government do this ? ?

The basic premise is invalid--there is no such law in California. Is, perhaps, the question to be debated whether, IF California adopted such a law, it would be constitutional? I don't think that is a very good debate subject, since the answer is that it would be clearly unconstitutional under many provisions of both the Bill of Rights (freedom of speech and the establishment clause immediately come to mind) as well as California's constitutional right of privacy. Nobody could rationally argue the contrary and the point of a debate is to have reasonable arguments on both sides.