With public bathrooms I don't even care what's the gender of the person in the next stall.Nore should they care about my gender or sex.It doesn't need to match the sign on the door.
Since you do your business in a closed stall it doesn't matter.
I have no problem going to the ladies bathrooms just like I have no problem with ladies going to the men bathrooms.
I have seen moms take their young boy to the men bathrooms just like I have seen dads take their young girl to the ladies bathrooms.
Nobody has a problem with that so I assume it will be the same with gender.
And that's fine when people adopt such practices as their way of life on their own. Would you agree with the government or a bureaucrat in some agency somewhere demanding you do it in your business or your school? And if you don't comply, you may be subject to fines, loss of funding, etc?