Money the imitator makes is not a particularly meaningful factor in any of the relevant laws, outside of poisoning the explicit exceptions for fair use that fan fiction isn’t.

Fan fiction isn’t legal (excluding scenarios where an author explicitly blesses it, which has happened). It’s identical copyright infringement to use someone else’s character in your own work whether you get paid for it or not. It’s just generally not worth pursuing and alienating your most enthusiastic fans for most creators/companies, especially when there’s no money involved.