The problem here is the singling-out of an individual (the dead soldier and his family) who has taken reasonable means to avoid becoming a public figure.
Now if Ellen Degeneres or General Patreus dies and they want to protest the funeral, so be it. If they want to protest the Pentagon, CIA building, White House or even their local military recruiting station, so be it.
I'd even say that if the dead soldier was unusually decorated or unusually publicized, this funeral may indeed be fair game for singling-out.
The constitution has to work both ways. One person's freedom to political expression cannot impinge upon another private individual.
(p.s. I do concede this specific case isn't a good one because the dad didn't witness the protest while the funeral was happening. They should pick another case and chase it all the way back to the supreme court)