The issue before the Court isn't a pure free speech issue. There was no governmental entity curbing the church's speech, and the 1st Amendment only protects against governmental interference with expression. What is really being debated is how far the "public figure" exception can be stretched in personal injury suits. I would bet Scalia and Thomas will be looking at rolling back earlier decisions that made it harder to bring libel, defamation, and other injury suits against people for harms caused by another's speech.
The family in the lawsuit sued the church in civil court for intentional infliction of emotional distress. Traditionally, the 1st Amendment didn't protect an individual from being sued by another individual for the harm caused by the speaker's words. More recently, the Court did create a defense to some of these torts for speech about public figures. It used the 1st Amendment as justification for the exception. So, one of the issues before the Court in this case is whether the family members were public figures, triggering this defense/heightened burden of proof. Based on some public comments that Scalia has made in the last month, it doesn't sound as though he agrees with the public figure exception, and he would allow personal injury suits between private individuals to proceed based on the hate speech.
I don't know where Fred Phelps went whackadoodle, though. This is a man who spent his early legal career fighting for civil rights and equality. Then he lost his mind. The family has become so consumed with spewing hatred, they forgot about all of the good that they initially fought for. What happens to people?!?!