That makes no sense at all. The fact that schools are state schools does not imply that headteachers cannot set some rules. Especially this new law does allow

That makes no sense at all. The fact that schools are state schools does not imply that headteachers cannot set some rules. Especially this new law does allow exceptions which schools can set in their own rules. The fact that a law was passed means that this will apply to all schools, state and private. It's in fact explicit in the text of the law. Private schools are also "ruled by law"...