Thank you so much for this question—I did not realize that this theory was a thing, but it is!
From what I was able to find, there are a lot of people hung up on the fact that the prefect is aware of present-day-earth things like smartphones and holidays like Tanabata ( https://twitter.com/YuuRei20/status/1556750150600499200?s=20&t=jhRGOIpgEKx7XfkHdHKiTg ) and yet they do not know who Mickey Mouse is. If the prefect really is a normal human coming from a country on present-day-earth where smartphones are prevalent, they would know Mickey Mouse.
(Ref: https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q12263037682 )

(In the novelization and the manga series all three prefects are literally 16-year-old Japanese high school students, but it is still to be seen if they know that Disney is a thing or if they exist in Disney-less AUs.)

The game goes out of its way to not assign too many physical attributes to the prefect, which one would assume is because it is meant to be a self-insert, but the prefect’s goal is to go home. To the player, this is the equivalent of our goal being to stop playing the game.

So the theory goes that wherever it is that the prefect wants to return to, it actually isn’t present-day earth. That would mean the prefect is not the player, and that opens the door to a lot of possibilities such as being another Disney character, potentially with a connection to NRC’s 8th dorm: Ramshackle.
(Ref: https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q13249490348 )

An abandoned dorm from Crowley’s time, it was presumably based on a Disney villain much like the Queen of Hearts or Hades, we just don’t know which one or what happened for it to be abandoned and filled with ghosts that no one wanted anything to do with.

Before the Glorious Masquerade event there were rumors it could be based upon Hunchback of Notre Dame (because of the gargoyles) and there are those who guess that maybe it was based on Captain Hook from Peter Pan, as a classic movie that seems to have been conspicuously skipped over.
(Ref: https://twstsoku.com/archives/12388428.html / https://twstsoku.com/archives/23727601.html )

Others, however, are guessing 1940’s Fantasia (for those who do not know, the magician in “The Magician’s Apprentice” is named Yen Sid, the backwards (or mirrored) spelling of “Disney.”
(Ref: https://twitter.com/jojo_mochi/status/1325106707677159425 )

It has been established that Mickey has a dream-connection to Ramshackle and seems to be occupying a room based on 1936’s “Thru the Mirror” (which is also referenced in Ignihyde https://twitter.com/YuuRei20/status/1576134151903752192?s=20&t=6sTsXyRS0QM7klzNb2CFNw). Mickey also makes an appearance in Fantasia, as a magic user.
https://twitter.com/mirrormazeworld/status/1650029237217423361

And there is a place for the prefect in Fantasia: the composer, a human who is only seen in silhouette and interacts directly with an animated Mickey Mouse.

Back to the topic of the prefect being a type of Fae, user @minnminnzemito has written an amazing blog post on the topic (https://note.com/takotako095/n/ne5f379511dca) that they gave me permission to summarize and share in English:

They also make the connection between Fantasia and Ramshackle and theorize that both Grim and the prefect share the motif of the Chernobog (“two halves of one student”). Chernobog is referenced in-game as “the ruler of the monsters of Bald Mountain” and in Fantasia it disguises itself as an inconspicuous mountain when it isn’t hosting demon raves, much like prefect seems most unassuming. For now 👀

minnminnzemito explains that a shapechanging Prefect would make everyone’s interpretations in things like the official profile template recently released by #twst_jp ( https://twitter.com/disneygames_jp/status/1647805964375187457 ) canonically accurate: demons hardly need be restrained by things like what age/gender they appear to be.

In other theories it is guessed that the mastermind behind the overarching drama at NRC is either Malleus or Crowley himself, but this theory suggests that it is actually the prefect, and Crowley is acting at their behest (it is insinuated that the prefect may have lost their memories).

According to Wikipedia the Chernobog seems to have a complicated history and may or may not be an evil deity from the 12th century (its name literally means “Black God”), and #minnminnzemito says this may be hinted at by the names of the two prefects in the Twst manga, both of which have connections to the afterlife of two different religions.
https://twitter.com/minnminnzemito/status/1603714408412155904

(More about the names of the prefects in the manga here https://twitter.com/YuuRei20/status/1628566979820032000 )

Bonus: #minnminnzemito has also created a compilation of all the hints we have received throughout the game as to what the prefect looks like (shared with permission): https://note.com/takotako095/n/n6999ac5dfd7c

Including being (perhaps significantly) smaller than Floyd with shorter legs than Vil, black hair and more.