WASHINGTON—The Supreme Court on Friday said it will decide whether states can deny permission for specialty license plates because a proposed logo or message may be offensive to the public.

The court said in a brief written order it would hear an appeal by Texas, which in 2011 rejected a proposal by the Sons of Confederate Veterans for the creation of a plate with a square logo of the confederate battle flag.

In rejecting the proposed plate, the state’s Department of Motor Vehicles Board said many members of the public reasonably associated the confederate flag with expressions of hatred or bias against minorities.

The Sons of Confederate Veterans sued, arguing the state’s stance violated the group’s First Amendment free-speech rights because the state issued specialty license plates designed by other organizations. This, the group said, amounted to what is known as impermissible viewpoint discrimination by the government.

A federal trial judge sided with Texas, ruling the First Amendment didn’t require the state to endorse the confederate flag by placing it on government-controlled property. The Fifth U.S. Circuit Court of Appeals reversed that ruling and sided with the Sons of Confederate Veterans in a split decision earlier this year.