Well, if we want to get back to the OP, the whole disclosing-fantasies-in-public thread is just a distraction. The real question in the OP is about identity.
What is part of your identity, what makes you you? What can be taken away from you with you remaining you and what, if taken from you, will create someone else in your place?
Can we rephrase that so as to avoid Ship of Theseus issues?
Which future do you prefer? The future which contains a being which is very similar to the one you are presently, or the future which contains a being which is very similar to what you are presently +/- some specific pieces?
If you answered the latter, what is the content of "+/- some specific pieces"? Why? And which changes would you be sorry to make, even if you make them anyway due to the positive consequences of making those changes? (for example, OPs pedophile might delete his pedophilia simply for the social consequences, but might rather have positive social consequences and not alter himself)
There's a recent science fiction story that I can't recall the name of, in which the narrator is traveling somewhere via plane, and the security check includes a brain scan for deviance. The narrator is a pedophile. Everyone who sees the results of the scan is horrified--not that he's a pedophile, but that his particular brain abnormality is easily fixed, so that means he's chosen to remain a pedophile. He's closely monitored, so he'll never be able to act on those desires, but he keeps them anyway, because that's part of who he is.
What would you do in his place?
In the language of good old-fashioned AI, his pedophilia is a goal or a terminal value. "Fixing" him means changing or erasing that value. People here sometimes say that a rational agent should never change its terminal values. (If one goal is unobtainable, the agent will simply not pursue that goal.) Why, then, can we imagine the man being tempted to do so? Would it be a failure of rationality?
If the answer is that one terminal value can rationally set a goal to change another terminal value, then either