Transgender individuals will get to choose whether to use male or female bathrooms and locker rooms in city facilities under an executive order signed Monday by Mayor de Blasio. The city’s estimated 25,000 transgender residents can freely use the facility “that most closely aligns with their gender identity or expression without being required to show identification, medical documentation, or any other form of proof or verification of gender,” the order says. “They are part of the fabric of life in this city, and we honor them, and we embrace them, and we believe in them,” de Blasio said before at a Parks Department recreation center in Chelsea. “Too many transgender and gender nonconforming New Yorkers have been harassed. They’ve been made to feel out of place and uncomfortable.” The policy, which took effect immediately, requires city agencies to post the order conspicuously within the next three months, train managers within one year and report on steps taken to comply with it. Maya Wiley, the mayor’s counsel, said exemptions would be granted only under extreme circumstances, such as within the prison system.