Washington (CNN) -- A Kansas church that attracted nationwide attention for its angry, anti-gay protests at the funerals of U.S. military members has won its appeal at the Supreme Court, an issue testing the competing constitutional rights of free speech and privacy.

The justices, by an 8-1 vote, said Wednesday that members of Westboro Baptist Church had a right to promote what they call a broad-based message on public matters such as wars. The father of a fallen Marine had sued the small church, saying those protests amounted to targeted harassment and an intentional infliction of emotional distress.

"Speech is powerful. It can stir people to action, move them to tears of both joy and sorrow, and -- as it did here -- inflict great pain. On the facts before us, we cannot react to that pain by punishing the speaker," Chief Justice John Roberts wrote for the majority.

At issue was a delicate test between the privacy rights of grieving families and the free speech rights of demonstrators, however disturbing and provocative their message. Several states have attempted to impose specific limits on when and where the church members can protest.

The church, led by pastor Fred Phelps, believes God is punishing the United States for "the sin of homosexuality" through events including soldiers' deaths. Members have traveled the country shouting at grieving families at funerals and displaying such signs as "Thank God for dead soldiers," "God blew up the troops" and "AIDS cures fags."

Westboro members had appeared outside the 2006 funeral for Lance Cpl. Matthew Snyder in Westminster, Maryland, outside Baltimore.

Snyder's family sued the church in 2007, alleging invasion of privacy, intentional infliction of emotional distress and civil conspiracy. A jury awarded the family $2.9 million in compensatory damages plus $8 million in punitive damages, which were later reduced to $5 million.

The church appealed the case in 2008 to a federal appeals court, which reversed the judgments a year later, siding with the church's allegations that its First Amendment rights were violated.

Albert Snyder, Matthew's father, said his son was not gay and the protesters should not have been at the funeral.

"I was just shocked that any individual could do this to another human being," Snyder told CNN. "I mean, it was inhuman."

Church members say their broader message was aimed at the unspecified actions of the military and those who serve in it. They believe U.S. soldiers deserve to die because they fight for a country that tolerates homosexuality.

Roberts in his opinion noted the Snyder family was not a "captive audience" to the protests that were conducted several hundred yards away.

"Westboro stayed well away from the memorial service," wrote Roberts. "Snyder could see no more than the tops of the signs when driving to the funeral. And there is no indication that the picketing itself in any way interfered with the funeral itself."

Based on that the court concluded Snyder could not collect damages from Westboro.

But the chief justice showed little sympathy for the message Westboro promotes.

"Westboro believes that America is morally flawed; many Americans might feel the same about Westboro. Westboro's funeral picketing is certainly hurtful and its contribution to public discourse may be negligible," he said. However, "As a nation we have chosen a different course -- to protect even hurtful speech on public issues to ensure that we do not stifle public debate."

The ruling was a narrow one, dealing with the specific, unusual facts of this appeal. Such vocal protests at military funerals are almost entirely confined to this one small group. Roberts said on the free speech question, it was enough to rely on "limited principles that sweep no more broadly than the appropriate context of the instant case."

Only Justice Samuel Alito dissented. He said the church's "outrageous conduct caused petitioner great injury, and the court now compounds that injury by depriving petitioner of a judgment that acknowledges the wrong he suffered," he said. "In order to have a society in which public issues can be openly and vigorously debated, it is not necessary to allow the brutalization of innocent victims like petitioner."

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Church members told the court they have a duty to protest and picket at certain events, including funerals, to promote their religious message: "That God's promise of love and heaven for those who obey him in this life is counterbalanced by God's wrath and hell for those who do not obey him."

The congregation is made up mostly of Fred Phelps and his family. The pastor has 13 children, and at least 54 grandchildren and seven great-grandchildren.

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The case decided Wednesday is Snyder v. Phelps (09-751).

"outrageous conduct caused petitioner great injury, and the court now compounds that injury by depriving petitioner of a judgment that acknowledges the wrong he suffered," he said. "In order to have a society in which public issues can be openly and vigorously debated, it is not necessary to allow the brutalization of innocent victims like petitioner."