This exact question was asked on Yahoo! Questions in 2024, and here is the response:
・He has two older sisters and is made to do chores for them.
・He comes from a household where being “cute” is heavily emphasized.
・The spelling (of the names) is similar.*
・“Keito” (Kate) is a female name.
・There are scenes here and there that seem to suggest it. For example in the Ghost Marriage event, there was a scene where he had to return to the dorm by midnight.
・There are various theories about the origin of his unique magic, but the way he uses it to handle miscellaneous tasks resembles Cinderella reflected in soap bubbles during the song “Sing, Sweet Nightingale.”
・There is a line in his class voice where he says, “Professor Trein is so strict!” — and Professor Trein is based on Lady Tremaine.
Trein and Cater are also from the same country, with Cater being the only Heartslabyul member who is not from the Queendom of Roses.
This might also be an Alice in Wonderland reference as well, as the words “Ace,” “Deuce” and “Trey” all come up in the original Alice in Wonderland movie, but “Cater” does not: he is not from there.
And there are what might be considered additional “hints” to this theory in Riddle’s dorm uniform vignette, which revolves around Riddle helping Cater study for a practical exam.
After Cater fails to memorize a study guide that Riddle prepares, Riddle changes tactics and learns how to use Magicam, which Cater is infamous for paying a lot of attention to.
Riddle starts sharing pictures that do not make much sense to Cater, who wonders why Riddle is sharing photos of things like a broom and a rag, both of which Cinderella is seen using in the original animated movie.
In the vignette there is then a cut to Riddle, who uses the hashtag “FireplaceAshes” on a Magicam post that he intends for Cater to see, connecting directly to the name, “Cinderella” 📝
Cater also shares a birthday (February 4) with the voice actor of Prince Charming from the original movie, William Edward Phipps.
In the live-action adaptation of Disney’s Cinderella her father is a merchant who travels for work.
Cater’s father is a banker instead of a merchant but does travel for work, taking his family with him when he is transferred “about once every two years.”
There is a high-heeled blue shoe in the Heartslabyul birthday scene background.
It seems this was a very widespread and popular theory in 2020 right after the game’s launch, but maybe not discussed as often, recently.
※ This is a literal translation of the responder’s answer, possibly a reference to Cinderella and Cater both starting with the letter “C.”
Twisted Wonderland Reference Note 