The justices heard arguments Monday in a case in which they voiced concerns both about government censorship of people’s speech and offensive messages that could, at worst, incite violence.

Specialty plates brought in $17.6 million in Texas last year, and state officials said there are now nearly 450 messages to choose from.

The state rarely rejects a specialty plate, but it did turn down a request by the Texas division of the Sons of Confederate Veterans for a license plate with its logo bearing the battle flag, similar to plates issued by eight other states that were members of the Confederacy, as well as Maryland.