Customer Non-Discrimination Act This bill prohibits discrimination based on sex, sexual orientation, and gender identity with respect to public accommodations and facilities. 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. 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 also prohibits the provision of less favorable treatment with respect to pregnancy, childbirth or related medical conditions as compared to other physical conditions.