My understanding is that you can create an X account with a burner email address, and be fairly anonymous. Determined sleuths can probably still find out who you are, and certainly the various government officials can find out. However, the effort needed to trace and dox a private account like this is fairly high.
However if you want to get a blue check and monetize, then you have to give X your identity information, so they can deposit money into your bank account. You can still maintain an anonymous user ID, but it's more likely that hostile persons can find out who you are in that case.