The simple answer to the original question of this topic on my part would be no. Killing people for a) doing something wrong or b) having a specific disorder that makes them act compulsively in a way that's harmful to others is something I find quite unacceptable.
Humans are social creatures and most of us instinctively act in a way that's productive for our society. Some people don't, more often than not because they can't due to one form of disorder or other. Such members must be dealt with (for lack of a better word) appropriately for the society to function. By that I mean that they should be removed from the general population, but intentional murder is not and can not be an answer. They are people, just like everyone else, and they need the same opportunities as anyone else. If rehabilitation proves ineffective or impossible, incarceration is the appropriate answer (preferably in a mental institution, preferably indefinitely).
Killing child molesters is also counter-productive. By studying people with various potentially harmful disorders we can develop an early warning system and prevent abuse and protect the general public by starting rehabilitation early enough so the disorder doesn't manifest in a harmful way. By studying such cases (and trust me, corpses are quite unresponsive and therefore useless for research) we can eventually even develop treatment for it.
But try to look at it from another perspective - yours. You said you have a very specific mental disorder that can, in some cases, cause people to lash out and harm others. Should they be put to death as well if they for instance kill someone as a direct result of their disorder? Should delusions of people with schizophrenia be regarded differently than delusions of people with disorders you dislike?
Of course I'm not saying that the victims should just forget about abuse and leave their abusers alone. In such cases therapy is the way out. Someone else's death isn't. It never is.