The above instance would occur regardless of the policy but, because Target publicly stated their support for transgender folk, everyone is dreaming up the hide-your-wives-and-daughters-from-pervs-dressed-as-women scenarios.
They act like the women's restroom sign had a force field against anything with a Y chromosome & this will open the door for someone to 'take advantage' of gender identification.
Macy's reported an incident in which a man impersonated a woman, went into the ladies' restroom & was taking pics of women/girls in neighboring stalls. A woman became suspicious, notified management who then notified their security personnel. The guy was detained, arrested & charged with voyeurism.
This very scenarios would've happened regardless & the outcome would've been the same.
Do you really think someone wouldn't hear a child screaming in a restroom? Kids' voices reach decibel levels that could shatter glass.
Even if a perv waited until they were alone, someone could've walked in at any time & IF a parent is concerned, they should go in with the child or be right outside the door watching who goes in like a hawk.
@bkh: If that old lech asked me that, I'd look him straight in the eye & say "Let's call security & see what THEY think."