Whose public restroom does the law say this person gets to use?

There is a lot of backlash going on against states, primarily in the American South, passing laws that, among other things, require people to use the public restrooms that correspond to the gender the person was born as. Basically, you have an X and a Y chromosome, you use the men's room, and the law don't give a shit whether you think you're Marilyn Monroe. XX chromosomes? Women's room for you, no matter how much you dress like James Dean.

This makes sense to me. Without commenting on the validity of how the laws are written -- I haven't read any of them, and some or all may be too broad -- I fail to see how it can be controversial to require men to use the men's room, regardless of what they call themselves, and women to use the women's room, regardless of what they call themselves. I can call myself a fucking unicorn, and that doesn't make me one, no matter what surgery I have, nor does it require the state or anyone else to provide unicorn restrooms for me.

Crazy example? Maybe not. Consider this:

A male-to-female transgender woman who prefers the pronoun “it” says it believes it was born not only the wrong sex, but also the wrong species, and has been undergoing human-to-dragon transition procedures to fix the problem. The 55-year-old, who was born “Richard Hernandez” but now goes by “Eva Tiamat Baphomet Medusa,” has already had a whole slew of transformative work done: Tooth extraction, eye coloring, horn implants, ear removal (!), nose modification and a procedure to give it a forked tongue.

The individual in question is "pre-op," meaning he still has male genitalia. He cannot, of course, get rid of his Y chromosome and so will always be male regardless of what he chops off. You want this guy in the women's restroom? Fuck, I don't want him in the men's restroom. Wonder why?:

Yeah, no thanks.