Their position has no basis in fact. First, transgender women are not pretending. They are at great risk when using the men's room. Transgender men, for the most part, would never pass muster in a women's room. And, many women, including my spouse, are challenged on a regular basis when using the restroom because they do not present as a stereotypical female.
Other groups facing discrimination will be anyone who needs assistance with normal restroom activities.
These laws are being championed by people who are ignorant of the transgender community and the issues facing transgender men and women. Now that marriage equality is legal throughout the United States, these folks needed to find something else to occupy their time. It's too bad they could not have settled on something that is actually necessary.
Contrary to the rantings of these folks, there have NEVER been any incidents involving a transgender woman accosting a cisgender woman or girl in a restroom. That comes from law enforcement agencies around the country. There have been numerous incidents in which transgender men and women have been violently assaulted because of their gender identity.
The U.S. Department of Justice has filed a lawsuit against the state of North Carolina because that state's law violates federal laws, including Title VII of the Civil Rights Act of 1964, designed to protect transgender individuals from discrimination. U.S. citizens are not in danger from transgender men and women. Members of the transgender community, however, are endangered by these ignorant, transphobic and homophobic enactments by GOP led legislatures.
National LGBT organizations are gearing up to protect transgender rights around the country. Education will be the first place to start.