I think the younger you are the more likely you are to be certain My Immortal was written as a joke, partially because it’s the progenitor of pretty much all modern Bad Fanfiction Tropes, so when you read it now you think “oh they were trying to use as many bad fanfic tropes as possible, it’s clearly a joke” even though those tropes exist to make fun of My Immortal. My Immortal could have been written as a parody of bad fanfiction but it made such an impact on that subculture that it’s entirely possible that it only seems like a satire because it’s the original thing being satired.
My Immortal could’ve been an intentionally bad fanfic but that’s not a given. The uncertainty comes from the fact that My Immortal was written in a pre-My Immortal world, and the only reason it seems like a parody now is because we already know about My Immortal.
The other reason is “nobody talks like this, nobody writes like this, it has to be someone making a joke” but the thing is, I was a moderator on a fanfic site when My Immortal dropped, and yes, they really really did talk like that. There is not a single line in My Immortal that would’ve been out of place in 2006.
I should say that Mary Sue parody fics had been done before – hell, the name comes from a fic from 1974 – but never, at least to my knowledge, with that level of dedication and immersion. This wasn’t just a oneshot, a little “teehee, look how silly this overpowered, ridiculously-named character is!” fic. This was 44 chapters long, each with a fairly impressive wordcount, an IRL sideplot (an argument between the author and her beta reader that caused a visible drop in spelling), and accounts on multiple websites, including Quizilla.
Like, there’s trolling and then there’s trolling, and if it was indeed a parody, it was done with a level of mastery that would be impossible to recreate now.
I strongly suspect that the authorship and authorial intent of My Immortal will one day be as hotly contested within academic circles as that of Shakespeare.