Simple solution to the whole mess, no need for laws, initiatives, snark, religion, politics, or any other handwringing or disrespect for people on BOTH sides of this argument:

Just eliminate the Public part of the 'Public Bathroom'. Enclose each stall with walls and a door. They have these kinds of stalls in the Davenport Hotel in Spokane, Washington. Absolutely beautiful place. Each bathroom stall is simple, a single toilet, walls, locking door. Perfect privacy, 6 in a row.  Anyone can use them, no one knows who's next door. No one cares. These stalls have been there since around 1920 I believe.This very idea was brought up in an Opinion article in the ADN a month or two ago, unfortunately I have forgotten who penned it. Make them single stalls with a floor mounted toilet and this whole nasty little ruckus goes bye-bye, just like that author recommended. No one else will be in there with you.