The gender neutral bathrooms I’ve seen in Seattle (at the airport and a library) have floor-to-ceiling stall dividers that don’t have cracks between the door and the divider and they just have a large shared sink. The one at the airport had urinals on the opposite side of the wall as the stalls so you had to walk around if you wanted to get to them, meaning nobody would accidentally walk to the urinals.

In short, gender neutral bathrooms are just more private. How horrific.