WINSTON-SALEM, N.C. (Reuters) - Transgender people barred under a new North Carolina law from choosing bathrooms consistent with their gender identity filed a federal lawsuit on Monday, arguing the measure was discriminatory and threatened their personal safety. North Carolina last week became the first state to enact a measure requiring people to use bathrooms or locker rooms in schools and other public facilities that match the gender on their birth certificate, according to the National Conference of State Legislatures.  “By singling out LGBT people for disfavored treatment and explicitly writing discrimination against transgender people into state law, (the state) violates the most basic guarantees of equal treatment and the U.S. Constitution,” said the lawsuit, which was filed by the American Civil Liberties Union and Lambda Legal. The state’s Republican-dominated legislature passed the law during a one-day special session called to repeal a Charlotte city ordinance that would have allowed bathroom choice based on gender identity versus sex at birth. State lawmakers also voted to prohibit local governments from enacting anti-discrimination protections based on sexual orientation and gender identity.  The actions drew swift criticism from lesbian, gay, bisexual and transgender advocacy groups and companies including American Airlines, Apple and Google.  In response to the law, the mayors of San Francisco and Seattle as well as New York Governor Andrew Cuomo have barred non-essential, publicly funded government travel to the state, saying the law is discriminatory. North Carolina Senate leader Phil Berger and House Speaker Tim Moore, both Republicans, said they were confident the law would be upheld in court. “This lawsuit takes this debate out of the hands of voters and instead attempts to argue with a straight face that there is a previously undiscovered ‘right’ in the U.S. Constitution for men to use women’s bathrooms and locker rooms,” they said in a joint statement. State lawmakers have warned of the dangers that could result from men sharing bathrooms with women and young girls. But transgender plaintiffs said they would be vulnerable because making known they are transgender puts them at high risk of violence. “This is about more than restrooms. This is about my job, my community and my ability to get safely through my day,” said Joaquin Carcano, a 27-year-old university employee who is a plaintiff in the suit.  Chase Strangio, a staff attorney with the national ACLU’s LGBT Project, said on Monday the new law on bathroom access has “no clear enforcement mechanism.”  Opponents of the law criticized Republican Governor Pat McCrory, who is seeking re-election in November, for signing the sweeping legislation on the same day it was introduced. They noted the weeks of debate and review given to a Georgia measure that sought to strengthen legal protections for gay marriage opponents before Republican Governor Nathan Deal signaled on Monday he would veto it. “By contrast, what happened here in North Carolina was a farce,” said Chris Brook, legal director for the ACLU of North Carolina. 