Hard to say. NPR interviewed Rodney Smolla, Dean of the Washington and Lee University School of Law, about what's at stake. According to Wikipedia, Smolla is a well-respected First Amendment scholar who in 2002 argued Virgina v. Black before the U.S. Supreme Court, a case involving Virginia's cross-burning statute.
This issue is not whether the church has a constitutional right to express its message; it certainly does. The much tougher issue is whether it has that right at the funeral of a fallen service member. We have public spaces and private spaces in our society, and the free speech rights that we all enjoy in our public spaces don't always give us the right to intrude into the private spaces of others. A lot will turn in these cases on exactly where the protesters assembleCheck out the full piece by clicking the link below.
There is a line, and that line will be drawn in close proximity to the funeral events. That kind of division will divide the public space and the private space. Even though what the church engaged in here does appear to fall within the realm of the is hate speech, the church has a right to engage in that hateful speech unless it invades in someone else's privacy.
A jury found that it was an invasion of privacy, and the interesting question on appeal will be whether the first amendment allows us to treat what happened here as the kind of invasion of privacy that trumps free speech rights.
Hat tip: NPR