Should you not advocate for that internally?
Let's say you are an ally for someone who needs an affordance like a gender neutral facility, should you not speak up on their behalf?
HR can handle this easily by following the law and drafting appropriate policies. It does not need a big battle with an "ally" at all. That's what leaving politics out of the workplace means. An individual's issues should be left to the individual.
How is your access to a gender neutral restroom or shower facility? Do you have a quiet place to pray multiple times per day? If you need a place to breastfeed (not a restroom), is that something available? What about dilating post gender reassignment surgery? Does your workplace offer the same benefits to same sex partners? Do you have to take a badge photo, if so, what name gets used? Can you wear head coverings in your badge photo? Have you ever heard expressions like, "Let's see what's under the kimono" in a business meeting? How is wheelchair access to your site? Can I operate all the machines you use if I am blind (can I navigate to facilities? Use all the machines in the breakroom? etc.)?
Put that in the idea box all you want.
Policies follow the law first. If there are specific requirements then, like I said, that's up to the individual to discuss. These issues are not the concern of everyone else.
No company is forced to do anything beyond the law just as the individual is not forced to work for the company. If the issue is with the law then it should be changed through the appropriate avenues, not hashed out in the workplace.
Or are you talking about the washroom down the hall? That's just your typical company policy.
Quod non erat demonstandum
If you don't want to use the mens or womens, then just use the restroom with the wheelchair picture on the door. There's your gender neutral facility right there. Solved.