Harry and the Mysterious Curse of the Girl-Who-Lived/WMG

Harry really is a girl.

 * The curse actually makes muggles, squibs (but only sometimes, as seen with Mr. Filch) and Harry herself think she is a boy, while wizards and people exposed to magic -like Petunia, as hinted in the first chapter- aren't fooled and see the truth. The curse also distorts Harry's words whenever he tries to convince other people of the illusion, but only certain people  can hear the lies:
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.
 * ...Except this can't be the case because the whole premise is that Harry is a guy, but everyone thinks he's a girl.

Volotredi's Horcrux is the cause of Harry's curse.
The actual Point of Divergence is when Tammy Riddle was born as a girl, rather than as the guy we remember from canon. After her rise to power as Volotredi, she went around making her horcruxes, just like in canon. Just like in canon, she attacked the Potters and failed to kill their infant son, Harry. When Volotredi's soul split accidently and formed the Harrycrux, the magic involved made it so that Tammy's gender perceptions overrode Harry's, and made everyone believe that he was a she. We know very little about soul-and-horcrux-related magics, but we do know that Voldemort/Volotredi was very powerful, with an ego to match. We also have no idea how a horcrux formed by a witch/wizard of one gender would react to being placed in the living host of another gender. In canon, we only see Harry (same gender), Nagini (different species, with gender perceptions never playing a role to the snake, only being referred to as a "she" rarely and incidentally), and the other horcruxes (inanimate objects). The magic would have to have been powerful enough to rewrite actual documents, as well as memories of the one-year old Harry as being "Harriet". But considering how the staircase to the girls' dorm could be fooled (possibly the way described in the above WMG, with magic reacting to both Harry's and Volotredi's wills, this could be the case with people's memories, documents, and other such things.

Dumbledore, Luna, Ollivander, and the Sorting Hat weren't affected because they are in no way intimidated by Volotredi's indomitable will. Squibs and those like Petunia (exposed to magic and with muggleborn relatives) see both personae due to not being primarily magical (and thus mostly unaffected). In time, as Harry becomes stronger and asserts himself over the Dark Lady, he will be able to "will" his male persona into existence, causing much confusion at first since it will likely take practice, and thus result in "Harry" appearing and disappearing occasionally, though few will make the connection between Harry's appearances and Harriet's disappearances. This will lead to several humorous misunderstandings, such as the girls waking up Harriet in her bed and discovering Harry there, and possibly Snape's shock at seeing James appear out of nowhere - with Lily's eyes.
 * Volotredi's anagram indicates that her name was probably "Tori Riddle" but yeah, this works.
 * Not unless her middle name changed as well(she needs a y in order to spell Lady). But that's entirely possible, all things considered.