True, what the symbols represent will remain whatever is done to them. Conversely, by the very nature of their being potent symbols, what is done to them is done to that for which they stand.
It depends in part on how important the thing represented is to an individual and the intent of the part committing offense to the symbol.
The Founders of the USA weighed serious concepts when attempting for forge this new nation, and they were living in an interesting time when there were many fascinating ideas and theories floating about. And they were, let us be clear, intellectual giants, nearly all of them. Well-educated, deeply philosophical, open-minded and (although some consider this an insult) free thinkers.
One of the first concepts to become part of the foundation of our nation was that we are a "nation of laws, not of men" (John Adams). For the rights of citizens to be respected, they must be universal and not subject to infringement either by government for the sake of oppression or convenience of governance, nor by individuals whose honor has been besmirched.
This means no support for honor killings, which we see even today in less enlightened nations. It means no duels, although we had a hard time giving that up even at that time - consider that our own Alexander Hamilton was shot dead in an illegal duel with Aaron Burr. It means we must give our respect to the law, even over the respect we show ourselves and our honor, when circumstances demand it. This is the hard path, is it not?
But this was the age of Voltaire, and our Founders were not immune to his logic when he was (falsely) quoted as having said ""Monsieur l'abbé, je déteste ce que vous écrivez, mais je donnerai ma vie pour que vous puissiez continuer à écrire" http://en.wikiquote.org/wiki/Voltaire, which was itself later paraphrased as "I may not agree with what you say, but I will defend to the death your right to say it."
We in the USA have the advantage of youth. We did not inherit all of European traditions, nor their notions of personal honor, insult, revenge and vendetta (we certainly managed to hang onto some of it, e.g., the Hatfields and the McCoys). And while Europe has divorced herself from some of the more bloodthirsty rituals of it's past, it has not been given the opportunity to remake itself en toto.
From the extreme of honor killing and duels to the less odious banning of hurtful speech, we have for the most part rejected such notions completely in the USA. But it is difficult.
We do recognize limits, especially that speech which is likely to precede life-threatening actions, such as inciting to riot. And depending upon the time, place, and nature of the speech in question with either Westboro or your example, either might have been justly seen as such. We recognize the rights of property owners to limit the free expression of speech on their own property by controlling access to it - ie, ejecting sign-wavers from their private property. We even, at times, impose lesser sentences on those convicted of crimes which stemmed from extreme duress and emotional pain, in recognition that both honor and emotional pain can drive one to criminal behavior who might otherwise never have taken such action. But we do not exonerate, nor hold apart from the law such behavior. We cannot deny that lynchings and rough justice have existed and sometimes still exist outside the law, but they law does not recognize laws of retribution or insult to honor or emotion.
Dickens said "The law is an ***" in the novel "Oliver Twist," and he was right. The law is ignorant of how much pain an action causes or does not cause; an action is either legal or it is not, regardless of how the action makes you feel.
Is it wrong for the USA to be so slavishly devoted to the notion of law taking precedence over emotion, ink and paper over people's feelings? I don't think so, but of course it always depends upon whose ox is being gored. When one is objecting to the notion of a woman put to death because her husband found she was not a virgin or unchaste after marriage, we might well consider such laws horrific and despicable. When laws require that a religion's founder's name not be blasphemed, we scoff (although there were laws against blasphemy even in the USA until not that long ago). When someone burns a flag and we find it is a legal and even protected form of speech, we're furious that such an insult would be permitted. Much like a devout or conservative Muslim might think it insulting that a person be legally allowed to desecrate a Koran, eh?
When one accepts the notion that an activity can be legally banned because the majority objects to it, then one must accept that any such activity can be banned because the majority objects to it, no matter what that activity might be. Our 'civil liberties' are written into the Constitution as prohibitions against the federal government rather than statements of actual rights precisely because we wished to draw a bright, clear, line which said "here the government may not trespass." And that means even when the majority have their feelings hurt, their honor impinged, or their pride trampled upon.
This we have. Most other nations do not. And we see the result. One may prefer the latter to the former, and I understand that. But it comes with risk, which I personally do not prefer.