The 2021 IPC Section 403.2 and IBC 2902.2 will allow group toilet rooms to be gender-neutral. Urinals can either be in an area visually separated area from the remainder of the facility or each shall be located in a compartment.
The code language that will be printed seems way too vague for having all genders in the same facility and for privacy. Almost anything goes as far as partition and door heights are concerned.
For water closets or urinals, I suggest floor to ceiling compartments with solid, full-height, lockable doors and occupied indicators. Undercut each door no more than ½" for exhaust make-up air and for best privacy. Do not specify louvered doors.
For safety in gender-neutral, group facilities, I might suggest that the toilet room have a back wall, sidewalls and an open front leading into common areas like egress corridors or break rooms. Put an island of shared lavatories between the room opening and the compartments. This may need approval by a local code official as lavatories are required to be in toilet rooms per the 2018 IPC 405.3.2 yet no definition of a toilet room exists in Chapter 2. So an open front 'toilet room' may need approval.
This might be best practice instead
Gender-neutral, single-user toilet rooms are defined in the 2018 and 2021 IPC 403.1.2 and IBC 2902.1.2. These are probably an even better and safer way - see attached drawing.
When clustered in one location and the doors opening into common areas, single-users can require less square footage than a gender-neutral, group facility. If not clustered, each single-user must be accessible per the first sentence of IBC 1109.2 (Exception 3 allows a 50% reduction in accessible toilet rooms when clustering).
Gender-neutral facilities solve state bathroom bills (transgender issues), provide potty parity, accommodate opposite-sex parent-caregivers and can reduce floor area. Privacy like this can also help the massive 14.4% of the population with Paruresis (Wikipedia) to better function in society.