We're pretty lucky to live in a province with a small population, so my proposal may not work everywhere.
But, in short, if I were premier and had a majority government, I would legislate to phase out shared-use facilities altogether. Around here, most washrooms only had two toilets and in the men's washroom, maybe three urinals, and not a whole lot of traffic (even less since COVID-19).
If you de-pluralise them, that nullifies any need for gender assignment.
I know, it's easier said than done, but it's an idea.