Yet you earlier stated that you would chaperone your young daughter into a gender neutral restroom. If these mentally ill/morally confused people are "generally not a threat", then that wouldn't be necessary.
Given that your original statement was for a6 year old girl, yes. She is going to be chaperoned every place she goes. She's 6. At that age she needs close supervision. As she grows up, she will need less and less. Not that hard to figure out.