Equality Act This bill amends the Civil Rights Act of 1964 to include sex, sexual orientation, and gender identity among the prohibited categories of discrimination or segregation in places of public accommodation. The bill defines: "sex" to include a sex stereotype, sexual orientation or gender identity, and pregnancy, childbirth, or a related medical condition; "sexual orientation" as homosexuality, heterosexuality, or bisexuality; and "gender identity" as gender-related identity, appearance, mannerisms, or characteristics, regardless of the individual's designated sex at birth. The bill expands the categories of public accommodations to include places or establishments that provide: exhibitions, recreation, exercise, amusement, gatherings, or displays; goods, services, or programs, including a store, a shopping center, an online retailer or service provider, a salon, a bank, a gas station, a food bank, a service or care center, a shelter, a travel agency, a funeral parlor, or a health care, accounting, or legal service; or transportation services. The bill prohibits "establishment" from being construed to be limited to a physical facility or place. The Department of Justice (DOJ) may bring a civil action if it receives a complaint from an individual who claims to be: denied equal utilization of a public facility owned, operated, or managed by a state (other than public schools or colleges) on account of sex, sexual orientation, or gender identity; or denied admission to, or not permitted to continue attending, a public college by reason of sexual orientation or gender identity, thereby expanding DOJ's existing authority to bring such actions for complaints based on race, color, religion, sex, or national origin. The bill revises public school desegregation standards to provide for the assignment of students without regard to sexual orientation or gender identity. The bill prohibits programs or activities receiving federal financial assistance from denying benefits to, or discriminating against, persons based on sex, sexual orientation, or gender identity. The bill prohibits employers with 15 or more employees from discriminating based on sexual orientation or gender identity, subject to the same exceptions and conditions that currently apply to unlawful employment practices based on race, color, religion, sex, or national origin. Employers must recognize individuals in accordance with their gender identity if sex is a bona fide occupational qualification that is reasonably necessary to the normal operation of that particular business or enterprise. The bill provides government employees with protections against discrimination based on sexual orientation or gender identity. DOJ may 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. The bill amends Fair Housing Act, the Equal Credit Opportunity Act, and jury selection standards to add sexual orientation and gender identity as classes protected against discrimination under such laws.