This protects no one. Some people are trans, and they are at risk of experiencing targeted harassment and violence. All this does is put at-risk people at even greater risk. 

Right now, people who present and move through life as male or female group themselves appropriately into their respective changing areas. This petition would force some female-presenting people into male-exclusive spaces, and it would likewise put someone who looks altogether like a man into a room full of changing women. I cannot imagine that is what is desired -- why are you not seeking to protect women, or trans people? Why are you thoughtlessly endangering both?