There are hundreds of cities, dozens of states and even whole countries that extend protections to transgender people to include the ability to use the proper restroom. Many of these protections have been on the books for decades and none of the things you are imaging has happened, ever. There are zero instances of a woman who happens to be transgender molesting anyone in any bathroom. These bathroom bills have nothing to do with protecting anyone but rather creating convenient scapegoats to score cheap political points with the conservative base. Don't take my word for it , here is the official position consensus statement from hundreds of organizations dedicated to protecting women and children.
http://4vawa.org/