If the player has a case, I'd think it would stem from legal limits on the extent to which an organization's people are allowed to contractually sign away their rights to engage in "immoral" behavior when "off the clock."
Under what circumstances is an organization allowed to impose its notions of "morality" on its people when they're "off the clock"?
To me, part of the question is whether you're using the organization's resources or branding. If the OnlyFans channel mentions the Olympics or his team by name, or uses its logos, or he makes videos during the times he's officially "on the clock" for training, my instinct is that they have every right to object.
But if he's using his own name, or a pseudonym, staying "off the clock" and not displaying any Olympics or team branding, it's less clear.
(Thought experiment: If LeBron James started an OF side hustle, would / should the NBA be allowed to come down on him? If your answer's different from this case, what makes the situations different?)
He's a sympathetic character -- they tell people "You need a ton of money to compete here" [3] so he says "Well that sucks, my family isn't rich, I don't really have the skills or free time to get a job at FAANG, but I guess I can hustle the money on OF" and then they suspend him for doing it -- but he's only doing it trying to get through the obstacles they created.
(OTOH, if a bunch of skilled but poor athletes started taking the same path, would it damage the Olympics brand if people started to think "The Olympics? You mean those sports teams where the players all sell their bodies online to pay their team dues?")
[1] This seems super vague. If you and I sign a contract that has a clause saying you won't engage in offensive behavior, if I want out of the contract I can always trap you by, say, walking through a doorway at the same time as you do. If you don't hold the door for me, that's offensive behavior -- you let it slam into my face, you impolite uncultured swine! If you do hold the door for me, that's offensive behavior -- it's clearly a form of gendered violence and sexual harrassment, you sick perverted swine! No matter what you do I can always claim your actions were "offensive" or "immoral," so I can get out of the contract, and hit you for breach-of-contract penalties to boot.
[2] If a contract forbids you from "indecent" behavior, does that mean you can't engage in any form of sexual activity whatsoever for the duration of the contract?
[3] To me, this seems counter to the spirit of the Games. I always thought the Olympics were supposed to be a contest for amateur competitors -- but most of the teams seem to be professionalized outfits with very expensive training. (I know very little about sports.)