Mom and Pop actually probably have a much better setup than a lot of places already. Many small businesses have a single occupant male and female bathroom. Change signage to just "bathroom", have at least one with a changing station and make sure they both meet ADA compliance (which is technically already law) and require working locks.
If bathroom safety is SO very important that you feel it is worth discriminating against people and allowing them to be harassed because they don't fit your mold of what makes a person male or female, then maybe it's worth people footing the bill for that level of safety.
OR you can just choose to believe stats that are readily available about how transgender people are currently treated everywhere and how anti-discrimination laws have helped alleviate these and admit, it isn't about safety. It's about the fact that transgender people make you feel funny and you don't want to admit anything that would normalize them, like them having the same rights as everyone else.
If you are honestly interested in some of the statistics and what can be done, this is a great start.
http://transgenderlawcenter.org/resource...g-in-peace
As for a medical definition, what do you want? How about something like intersex? Conditions like androgen insensitivity syndrome are one of these. In utero, the fetus has XY chromosomes, which would typically be male. However, something happens and the fetus cannot do anything with the male hormones. Develops physically as female. Looks female and many don't realize until puberty that they have no uterus or ovaries. Chromosomes say XY, male, but by our definition by looks, would appear to be female. Intersex conditions are not as rare as once thought. It wasn't tracked and social stigmas still make it difficult to get accurate numbers. Estimates are like 1 in 1500 or 1 in 2000 births. May be even more common though. And these are the KNOWN ones.
What gender do you want to put on the birth certificate for a baby born with Androgen Insensitivity Syndrome? What bathroom do you want that child to use?
And again I ask, what standard do you want to use to determine bathroom use? The genie is out of the bottle. We can't ignore the fact that transgender people had to create websites and apps to give them lists of safe bathrooms. That bathrooms were inherently unsafe for most transgender people all over the county. Laws like HB2 just cannot be enforced in a sensible way. We can't go back in time.
You propose paper? So who pays for the potty police? You think it's horrible to get mom and pop to upgrade the bathroom? So they need to hire a bathroom guard instead?