In my opinion, a two bathroom solution IS the answer: One for those who want absolutely privacy, and one for those who don’t. To elaborate, one all-inclusive bathroom for anyone who wishes to use it, regardless of gender, and one private bathroom for those with privacy concerns, regardless of what those concerns may be. Would the line for the private bathroom be longer? Maybe, but that’s the price you pay for privacy.
I have always preferred single-seat restrooms. I don’t like using the restroom with anyone else, regardless of their gender. However, if forced to use a community restroom, I don’t care who’s sitting in the stall next to me. Many people do care, however, and protecting one person’s rights at the expense of another’s is not equality nor freedom. Privacy is a right (as much as anything is really a “right”), and that includes not only physical privacy, but the privacy surrounding one’s need or motivation for said privacy.
Genderless bathrooms are not a new idea, and trying to integrate a more open minded view of gender identity into a very binary bathroom infrastructure is like putting a round peg into a square hole. No private space should be forced, by law, to do anything they don’t want to do (though most will certainly bend to the will of their customers, and society in general, if it might affect profit). Public spaces funded by tax money, however, should absolutely adhere to the most fair and equal solution possible.
Btw, I will never understand the practice of making two single-seat restrooms gender specific. Everybody knows that the line for the women’s room ends up being longer, so staggering the genders between two gender non-specific restrooms seems the most efficient practice.