Aren't you missing something here? LulzSec also claims to have a morally reasonable agenda. Indeed, LulzSec claims to be entirely in the right, morally speaking. Now, reasonable folks can disagree about whether they are actually in the right, but it's false to claim that they are not "pretending" or claiming to have a morally reasonable agenda. They are, quite clearly, making that claim.

To me, that's the definition of hypocrisy. They pretend to be acting from a moral (or at least societal) high ground and roundly condemn the actions of anonymous. However, both are engaging in the exact same behavior. Now that's hypocritical!

The FBI doesn't normally, and it is not their purpose to engage in the exact same behavior. 95% of the time, they act within bounds I suspect you agree with. I wouldn't consider the 95% hypocrites, only the 5%, and so I can't call the whole agency hypocritical, only parts.

Are you allowed to break into other people's property and use weapons to enforce your own system of rules on them? Nope.

Are you allowed to lock people in a cage for decades because they do something you disagree with? Of course not.

Is the FBI allowed to do this? Well, yes, but only because they're special and you have to do what they say, not what they do. Now what's this word hypocrite you speak of?