Same here, Jude.
My heart says a family ought to be able to conduct a funeral in peace. We curtail the freedom of speech in schools, e.g., students can't say things that interrupt the pedagogical climate. (I just read about a case in my textbook about a student who spoke during an assembly and then started spouting off obscenities and obscene material. It made the whole student body go wild, responding with obscenities and obscene gestures. He got punished by the school, then sued, saying his 1st Amendment rights were violated, but the courts found that it was reasonable for the school to punish him and silence him as he had disrupted the learning process and atmosphere.)
Likewise, teachers have guidelines within which they have to operate; there are just things they can't say--unless they have a very, very compelling reason (e.g., an important educational goal that can't be met in another way) to do so.
A very famous example is that it's illegal to shout "fire!" in a crowded building. So we have reasonable restrictions already on the freedom of speech, and I do not think they're frightening. I think they are common sense, and we definitely, as a nation, err on the side of allowing liberty in this area rather than curtailing speech.
So I guess I think this. These protesters do have the right to assemble peacefully; they do have the right to speak their minds (as ignorant and repulsive as they are). They just do not have the right, imo, to do so in a place that interrupts the family's grieving process during the funeral and burial. If they want to stage their protest several blocks away or in another part of town, so be it. But they should not be able to be seen anywhere by the family--not near the funeral home, not near their private residence, not along the route taken by the cars to the cemetery, not by the church, not by the cemetery, nowhere.
Do I think this is a matter for the SCOTUS?
I would've preferred to see it decided by individual states.