So anyone can self identify as anything and switch around on a whim?

Technically yes, but people don’t tend to do that because identity runs deep and the trends is to correct a wrong like a mind-body mismatch.

whats the determining factor?

It’s complex but it’s usually gender dysphoria.

If I get arrested can I say I’m a female and get put in a women’s prison for instance,

You’d probably go into the prison that matches your official documentation regardless of what you say.