Under the Incorporation Doctrine, which applies the protections of the Bill of Rights to the states via the Fourteenth Amendment, the action that would be illegal for a state to do is establish a state church.
The Establishment Clause of the First Amendment prohibits the government from establishing an official religion or favoring one religion over another. Therefore, establishing a state church would violate this principle.
The other actions listed, such as criticizing the commander in chief, taxing the people, and trying people for murder, are not prohibited for the states under the Incorporation Doctrine.