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For Mr. Snyder, the case is not about free speech but harassment. “I had one chance to bury my son, and it was taken from me,” Mr. Snyder said.

Forty-eight states, 42 U.S. senators and veterans groups have sided with Mr. Snyder, asking the court to shield funerals from the Phelpses’ “psychological terrorism.”

While distancing themselves from the church’s message, media organizations, including the Associated Press, have called on the court to side with the Phelpses because of concerns that a victory for Mr. Snyder could erode speech rights.

Associated Press writer Jim Abrams contributed to this report.