What’s not that simple? Yes, there are some unusual exceptions (e.g., chimeras/mosaics) where a person could have both “XX” and “XY” cells but most people either have a “Y” chromosome or they don’t, regardless if it’s paired with one or more X chromosomes (or the person has only one X, in the case of Turner’s Syndrome). In the case of a chimera, the testicle test would be a good alternative (e.g., if they have a male leg or arm but are otherwise female, then I’d say “female”). As for the external genitals and social sex classification, if the person is truly a mix or unclassifiable, I’d take that on a case-by-case basis and suggest that they should pick one or the other. Am I missing an option here?
No, you are not missing an option. What is not that simple is making a determination based on ambiguous external genitalia. You said, “I don’t want a person with a penis in the bathroom with little girls or a person with female genitals in the bathroom with little boys.” I say making that determination is not that simple. It is possible to look at a baby and say, “Aw, this little girls genitals are swollen from the stress of birth, maternal hormones, etc.” It is only as she gets older that things become complicated. Meanwhile, she’s been socialized as a girl. She ought to be allowed to use a women’s bathroom.