A thread of common misconceptions, for quick reference and pinning:
-No, MAPs are not trying to join LGBT.
-No, "MAP" is not an attempt to launder pedophilia. It's an umbrella term that includes Pedophilia, Nepiophilia, Hebephilia, and Ephebophilia.

-When we call Pedophilia a sexual orientation, we do not mean to imply that it should be treated identically to all other orientations. It is merely a description of how it functions from a psychological point of view. E.g., it is likely inborn, unchangeable, etc.

While asking what counts as a mental illness is an open-ended conversation, at least as far as the American Psychological Association is concerned, Pedophilia itself is not actually a mental illness, and it does not necessarily require clinical intervention. Per the DSM-5:

Oh, and the obvious one: not all pedophiles are child molesters (and not all child molesters are pedophiles!)