Regardless of how we feel about TikTok (I dont like it either for the same reasons)
The ban isn’t about privacy violations by the owning corporation or because of challenges or mental health, but rather that the US government (directly or by proxy through the owning corporation) isnt the one in control of the information collected or the algorithms.
Due to its younger user base and lack of US based corporate interests, things that US corporations would normally block, remove or downplay with their algorithms are allowed. This means the culture and information that would normally dissapear from US media and social media instead on tiktok tends to be much more liberal and available. On the other hand, information critical of china or contrary to their culture may be less visible, and your information is getting tracked by china instead of the us.
This difference was exemplified in the wake of the United Healthcare CEOs assasination. Traditional US media was extremely critical of the shooter, and dropped any presumption of Luigi’s innocence or deniability prior to the conclusion of his court case. Comments and posts were removed for displaying anything other than giving him the death penalty (hyperbole, but). They denied that there was a problem and downplayed peoples concerns with the US healthcare system and billionaires.
TikTok on the other hand (and smaller social media sites like on the fediverse) showed immense support for Luigi, and expressed their disdain for the US healthcare system and the ruling class.
Same for the war in ukraine, especially for the genocide in gaza perpetrated by Israel on the Palestinians.
The government and ruling class is upset that they dont have the personal and tracking information of TikTok users, that they cant control the algorithm, and cant ask the company to stop showing things that make them look bad or could potentially be used to create a movement against them. Its those very trends that travel quickly through tiktok that have the potential to be dangerous to them.
spoiler
I think the problem is underspecified: it doesnt define what happens if they get it wrong. If they get it wrong are they barred from exiting? Or can they make a guess every night? Whats stopping them from all saying blue and the boat leaving with 100 blue eyed people on night 1? Or do they only get one guess?
Also it would have saved more people if the guru had simply stated the counts they daw because everyone could count the other people and then see what color was missing (their own eye color) and they could have all left night 1.