WASHINGTON – The Supreme Court agreed Monday to decide the outer limits of free-speech protection for protests, and to rule on whether a dead soldier’s family can sue fringe religious protesters who picketed near their son’s funeral carrying signs that read: “Thank God for dead soldiers.”

Like the famous case of the American Nazis who marched in Skokie, Ill., the new case of anti-gay picketing at military funerals tests whether the most hateful protests must be tolerated under the First Amendment, even if they inflict emotional harm. In this instance, the victims were the family of Marine Lance Cpl. Matthew Snyder, who was killed in combat in Iraq on March 3, 2006.

When his family announced his funeral would be held in Westminster, Md., a Kansas preacher decided to travel there with a few followers to protest. In recent years, Fred Phelps, founder of the Westboro Baptist Church, has been protesting at military funerals around the nation because he believes the United States is too tolerant of homosexuality. Though kept distant from St. Johns Catholic Church and the cemetery, Phelps and his followers carried signs that read “God Hates the USA” and “Pope in hell.”

Phelps and his followers had also threatened to protest at at least three military funerals in Maine. They failed to show up at two of them, but two church members did protest down the street from the Portland funeral of Lance Cpl. Angel Rosa, who was killed in action in Iraq in 2007.

The Maine Legislature later passed, and Gov. John Baldacci signed into law, a bill making it a crime to accost, insult, taunt or challenge any person attending a funeral, burial or memorial service. At least 30 states have passed similar laws, some of which have been challenged on free-speech grounds.

There was no suggestion that Lance Cpl. Snyder was gay or that the protests even involved him directly. But after returning to Kansas, Phelps said on his Web site that Albert Snyder, the soldier’s father, had “taught Matthew to defy his creator” and “raised him for the devil.”

Snyder sued Phelps for invading his privacy and for an intentional infliction of emotional distress. A Maryland jury rejected Phelps’ defense based on free speech and awarded Snyder $10.9 million in damages. But a judge reduced the amount to $5 million.

Last September, the 4th U.S. Circuit Court of Appeals threw out the verdict, citing the First Amendment. The protest signs were “distasteful and repugnant,” but their words were wild and hyperbolic, the judges said.

The father appealed to the Supreme Court, noting that a family at a funeral is a “captive audience” and cannot simply turn away from a hateful protest. “Snyder had one (and only one) opportunity to bury his son and that occasion has been tarnished forever,” his lawyer said. “Matthew deserved better.”

The high court said it had voted to hear the case of Snyder v. Phelps in the fall and to consider reinstating the jury verdict.

It was one of two privacy cases the court voted to take up. The second involves scientists and engineers at the Jet Propulsion Lab in Pasadena, Calif. They raised privacy objections when they were told to answer personal questions about drug use as part of a background check.

The National Aeronautics and Space Administration owns the lab, and in 2007 it extended the background checks for federal employees to all of its contract workers, including those at the Jet Propulsion Lab. A group of 28 lab employees sued, and they won an exemption from the 9th U.S. Circuit Court of Appeals.

But the Obama administration appealed, saying this privacy ruling cast a doubt on the legality of all federal background checks. The court said it will hear the case of NASA v. Nelson in the fall.