This unisex bathroom “solution” was always ….well, stupid. Because it trampled on the common culture and religious sentiments. “Solutions” should only trample on other people if there’s no other way to achieve the goal.
The solution for this problem was always simple — use an ADA-like solution.
The ADA did not force buildings to immediately rip up existing facilities and install handicapped-friendly ones. They handled it in the building codes, and all those ramps were built over time, as public facilities needed maintenance work to bring their facilities up to code, the ADA enhancements were put in then.
So, this is rather easy. Set a regulation that all new public-use buildings must have one private unisex option per x many of occupants. And, when any older building requires facility maintenance necessitating an inspection, the building must be brought up to spec (iow, adding unisex options) at that time.
Easy peasy. Nobody gets ticked off other than the building owner that has to pay for it (they complained about cost when the ADA was passed, too.)