Equality Act This bill prohibits discrimination based on sex, sexual orientation, and gender identity in a wide variety of areas including public accommodations and facilities, education, federal funding, employment, housing, credit, and the jury system. Specifically, the bill defines and includes sex, sexual orientation, and gender identity among the prohibited categories of discrimination or segregation. The bill expands the definition of public accommodations to include places or establishments that provide (1) exhibitions, recreation, exercise, amusement, gatherings, or displays; (2) goods, services, or programs; and (3) transportation services. The bill allows the Department of Justice to intervene in equal protection actions in federal court on account of sexual orientation or gender identity. Protections against discrimination based on race, color, religion, sex, sexual orientation, gender identity, or national origin shall include protections against discrimination based on (1) an association with another person who is a member of such a protected class; or (2) a perception or belief, even if inaccurate, that an individual is a member of such a protected class. The bill prohibits the Religious Freedom Restoration Act of 1993 from providing a claim, defense, or basis for challenging such protections. The bill prohibits an individual from being denied access to a shared facility, including a restroom, a locker room, and a dressing room, that is in accordance with the individual's gender identity.