In a 5-4 decision, the justices said the license plate was government property and therefore not subject to free speech protections.
The Confederate Veterans group wasn't happy about the way the case turned out. Neither was the American Civil Liberties Union. Its legal director, Steven R. Shapiro, issued a stern statement in response to the decision:
"By allowing states to censor private speech they deem offensive, today's decision is a step backwards for the First Amendment."
The ACLU siding with a Confederate veterans group might have raised some eyebrows in political circles. The nonpartisan nonprofit tends to fall to the left of the political spectrum on most issues.
But when it comes to free speech, the ACLU has a long history of defending people and groups that share very few of its political values. Here are some prominent right-wing groups and people they've defended:
The National Socialist Party
This is one of the ACLU's most famous contrarian cases. In 1972, the National Socialist Party wanted to rally in Skokie, a predominantly Jewish community in Illinois -- where about one in six residents was a Holocaust survivor.
The government tried to block it, and the ACLU sued to allow the Socialist Party members to wear swastikas on their march. The case went up to the Illinois Supreme Court, and the marchers got their right to wear swastikas.
In 2012, the Ku Klux Klan wanted to adopt a highway in Georgia.
The state blocked its request, and the ACLU sued the state to help the KKK adopt its stretch of highway.
"We decided to take this case because it is such a clear violation of the speech rights of the group," said Debbie Seagraves, executive director of the ACLU of Georgia.
In 2014, the Patent and Trade Office ordered the Washington Redskins to retire their controversial logo of a Native American. The ACLU helped the Redskins appeal the decision, arguing "by authorizing the government to deny registration of certain marks because of a viewpoint-based determination about the character of expressive speech, Section 2(a) violates the First Amendment."
When conservative talk radio host Rush Limbaugh accused Florida officials of unlawfully seizing his medical records in 2004 (investigators were looking into his claim of doctor-shopping for prescription pills), the ACLU was by Limbaugh's side. It filed a friend of court brief for him.
"The precedent set in this case will impact the security of medical records and the privacy of the doctor-patient relationship of every person in Florida," ACLU of Florida director Howard Simon said.
When Chick-fil-A president Dan Cathy said in 2012 he believes marriage is between a man and a woman, city mayors in Boston and Chicago wanted to give the Christian-owned restaurant the boot.
But the ACLU very publicly had Chick-fil-A's back.
"Everybody has a right to spout off about same-sex marriage and equal rights," ACLU's Massachusetts director, Carol Rose, wrote in a blog post. "Mr. Cathy and those who share his views can have their shout, even if their views are bigoted."
The Westboro Baptist Church
The Kansas-based church believes God is allowing troops to be killed because the U.S. lets its citizens be gay. Its members frequently picket troops' funerals. But when Missouri tried to ban one such picket in 2006, the ACLU filed a federal lawsuit to allow it to protest at the funeral. And the group has continued defending the church ever since.
"It's because you simply can't blindly trust the government with the power to censor that the First Amendment grants all Americans, regardless of their views, the right to express themselves," wrote Chris Hampton with the ACLU's LGBT arm in 2010.
"We agree on the need for significant reforms to curtail government surveillance authorities, like some of those included in the Patriot Act," they wrote.
When Republican mega-donors Charles and David Koch announced a Koch-funded public campaign for criminal justice reform in March, the ACLU hopped on board, even though its more liberal members were uneasy about the alliance.
"There's always some unhappiness whenever you work with, quote-unquote, the enemy," ACLU's director Anthony Romero told The Atlantic's Molly Ball. But he said having the Koch brothers involved "gives legitimacy" to an issue the ACLU cares about.
University of Oklahoma's SAE frat
Also in March, the University of Oklahoma expelled two leaders of the university's Sigma Alpha Epsilon fraternity when a video was released of fraternity members chanting racial slurs and singing about lynching. The ACLU released a statement urging caution in the university's treatment of the students.
Ryan Kiesel, director of ACLU's Oklahoma office, said: As the fates of the students at the center of this controversy unfold, we encourage the administration to demonstrate their commitment to due process; for it is often in protecting the rights of the very worst, we are able to demonstrate our fullest commitment to justice."