WASHINGTON — Supreme Court justices seemed to struggle with the question of whether the father of a dead Marine should win his lawsuit against fundamentalist church members who picketed his son’s funeral.

The justices heard argument Wednesday in the emotion-laden case of Albert Snyder. His son died in Iraq in 2006, and members of the Westboro Baptist Church protested the funeral to make their point that U.S. deaths in Afghanistan and Iraq are punishment for Americans’ immorality, including tolerance of homosexuality and abortion.

Justice Ruth Bader Ginsburg said the question is whether the First Amendment must tolerate “exploiting this bereaved family.”