It will be steamrolled in court until it reaches the radical, ultra-conservative Supreme Court who will say that the Constitution doesn't mention cameras and has no opinion about filming, at which point the law will stand.
Strictly speaking, there is a legal mechanism to remove them, but it basically wouldn't happen short of them being a serial killer. It requires the house of representatives to pass articles of impeachment by majority vote, then the Senate to hold a trial presided over by the chief justice of the supreme Court, at which a supermajority vote would lead to removal from office.
