At least this law will be based on something real. Your sex does not change, while gender seems to be arbitrary and ever changing with some.
It will also help prevent John Q. Pervert from walking into the girls/womens changing room at H2Oasis unobstructed because he claims to identify as a woman that day. I don't know if this has happened in Anchorage but it certainly has in other places.
Also, private businesses should be able to make their own policies on this issue, if someone disagrees they should feel free to do business elsewhere.