This doesn't surprise me in the least. From the interviews I've seen, in the eyes of the Westboro Baptist Church they are trying to save people. They would categorize their mission as one of mercy and benevolence rather than hatred and bigotry. Their logic isn't even that complicated.
1) Being gay is a sin according to the bible (there are passages to support this as we all know, they they're old testament)
2) If you die having sins you have not repented for, you will go to hell (also supported, and a "normal" Christian concept)
3) Therefore, they're attempting to get into people's face in order to shock them into realizing that they're sinning in order to save them from hell.
The protesting at soldier's funerals makes sense too in a twisted way.
1) In the bible, God punishes nations that institutionalize and tolerate sinful behavior (Sodom and Gomorrah).
2) America is in the process of transition to acceptance of homosexuality (which is a sin in their view).
2) Thus they see anything bad that happens to America as a consequence of that (with biblical examples to back things up).
Are they idiotic in my view? Yes. I still think that they're slightly misunderstood; it's cynical to automatically assume that they do what they do out of hatred when they profess to doing it out of love quite often. Take their word for it, I think they're telling the truth, they're just that fuckin' crazy.