Since the Hazelwood ruling, how important is state law in determining the rights of student journalists?

It is very important. A state law in 1971 guaranteeing all students full protection under the First Amendment, every other state needed to make a decision after the ruling: Did they want to abide by the standard given in Hazelwood v. Kuhlmeier, or did they want to pass a state law providing more protection for student expression? After the ruling, in July 1988, Massachusetts became the first state since California to pass a law strengthening the First Amendment rights of students. The law provides that "the right of students to freedom of expression in the public schools of the commonwealth shall not be abridged, provided that such right shall not cause any disruption or disorder within the school." The following states that followed the suit and passed so-called anti-Hazelwood laws were Kansas, Colorado, Iowa, and Arkansas. However, it was also introduction to other states as well. The constitutions of most states have language that supports, to varying degrees, free expression.
source: http://www.firstamendmentschools.org/freedoms/faq.aspx?id=13014