Note: this response is not because of any love lost between me and the WBC. That's definitely not the case. I just fervently believe that trying to silence a group is not the way to go about combating their ideas.
Martin Robbins at The Guardian elaborates:
Anonymous have succeeded in generating yet more publicity for an organization which thrives on attention and frankly, like the BNP in the UK, gets far more media coverage than it really merits or deserves.(Hat tip to Tracy King for the link)
Meanwhile, their actions will have little impact on a collection of people who live together, protest at real world events, and use shock value to get mainstream media attention. It is naive to believe that hacking some websites can bring down this sort of group. The best thing anyone can do is ask the media to shut the fuck up about them.
And finally there's the sheer hypocrisy of it. Anonymous make a big deal about freedom of speech, calling themselves variously "the Voice of Free Speech", or "aggressive proponents for the Freedom of Speech." Which would be great, if they were, but are they?
Well no, compare and contrast with: "the propaganda & detestable doctrine that you promote will be eradicated [...] we will not relent until you cease the conduction & promotion of all your bigoted operations & doctrines." The self-appointed defenders of free speech want to shut down people's websites. Bang goes another irony meter.