You may be right about the appeal - I'm not a lawyer. But this speak of the verdict somehow trampling on the First Amendment is nonsense. Look, read the thing again:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
There's no law that these people are accused of having violated, this wasn't a criminal trial. Phelps and his bunch are free as ever to protest at will. All of them are. What they must realize is that there may be civil consequences to being blatant assholes, and that there's two ways to make a statement - the effective way, and the way of the berzerk sociopath. One stands a chance of making a dent, the other - well, will get you sued.
But not only do you have to look at the First Amendment but you have to look at all the court cases that are attached to it on the subject, both civil and criminal.
Sorry that you think it is nonsense but it is not. It is these types of cases that draw the very boundaries that courts use to define First Amendment rights, both civil and criminal. When cases like this come up, and a line is drawn [and an attorney points to this case as precedent] you might find your right reduced. Here is where it gets personal:
Some people take the right to speak, the right to speak out, the right to protest very seriously. You might be compelled to protest for Right to Life . You have that right. When you protest at the clinic you are rewarded by fulfilling your obligations to your principles. OR, you might find your house attached if you were to protest at a clinic and someone claimed severe emotional distress or worse [I know you like to call it a lifestyle decision that a jury would look differently on but that doesn't always fly as it is not always a lifestyle decision].
So, you may decide that, instead of standing on your principles and protesting you will stay home because you don't want to risk losing your house and having your wages attached.
Now, because of a legal protest at a funeral 1500 away from Tulsa you now have to decide whether to risk your families assets and your wages or compromise your principles, keep quiet and stay on the porch.
And that is why it is not nonsense.