Let's look at some of these motivations for doing so:
Revenge? Dude, he's dead. Just how effective do you think this revenge will be?
To teach them a lesson? Well, I can see this. However... a lesson such as this is best taught through humility, not humiliation. Let's be effective about it. These people haven't had to deal with a loss of life like this. They're simply ignorant of what it means to grieve. When Freddie Phelps dies... they're going to know what it's like to lose a father, a husband, and a leader. That's going to hurt... badly. If people leave them alone, they may learn to understand what grieving families are going through, and how utterly wrong it is that they do what they do. Now, if after all that, whatsername starts vomiting hate and hellfire on my tv screen again, then it's open season. I expect a rational individual to respond to her, asking if she believes Phelps died because 'God hates bigots'.
At the end, confronting them won't make them go away; but perhaps the humility caused by the sudden realization that they are just as mortal as everyone they've ever protested might cause members of their flock to rethink their actions. Best let that happen, rather than attacking them and ensuring they go on the defensive like they were being persecuted.
