It's not about respect for them though, is it? It's about showing respect for yourself. If you prove that you are capable of sinking just as low as they did, then you forsake any claim you had of being above them intellectually or morally, by emulating them you become them, only on the opposite end of the same see-saw.
The whole reason not to behave as they did is to prove to them how alone they truly are, they might care that a soldier dies because it gives them an opportunity to spew their hatred, but if no-one cares that a member of their family dies enough to, even after all they've done, react in the same way, it serves as an abject lesson that they achieved nothing with their hatred. If you give in and copy them, you justify what they did.
e: And to clarify, the biggest compliment people could pay the Phelps family is to behave as they did, after all those years of saying how disgusting, inhumane and insensitive their behaviour was, at the first opportunity to behave in precisely the same disgusting way it is grabbed with both hands. After all those attempts to silence and deter them from doing it, to leap at the opportunity only justifies what they did.