"Self ID" is about going down to DMV and changing your ID without a psychiatrist's sign-off.
No, it isn't. That's what
you think it
ought to be about, but that's not what it's
actually about.
In reality, self-id is about
1) removing any and all gatekeeping to being recognized as transgender, so that no medical condition or distress is required legally or socially
2) removing any requirement or expectation of transition of any sort, so that a male doesn't have to have surgery or take hormones or even wear female-typical clothing in order to be considered transgender both legally and socially
3) removing any expectation of a person who does not pass from having to provide documentation of their sex in order to access single-sex spaces
4) making it socially unacceptable to challenge a person's dedication when they verbally declare themselves transgender
5) not requiring any change to legal documents of any sort in order to be treated as if they're the opposite sex
Male prisoners in california being moved to female prisons generally haven't changed their marker on their ID at all - they've simply declared that they're "women" and that their gender identity entitles them to be housed with women.