Here in Colorado, it is black letter law.
Rule 81.2 - Sexual Orientation Definitions
(A) The term "sexual orientation," as defined in the Law, means a person's orientation toward heterosexuality, homosexuality, bisexuality, transgender status or another person's perception thereof.
(B) The term "transgender" means having a gender identity or gender expression that differs from societal expectations based on gender assigned at birth.
(C) The term "gender identity" means an innate sense of one's own gender.
(D) The term "gender expression" means external appearance, characteristics or behaviors typically associated with a specific gender.
(E) The term "covered entity" means any person, business, or institution required to comply with the antidiscrimination provisions of the Law.
Rule 81.11 - Gender-Segregated Facilities
(A) Nothing in the Act prohibits segregation of facilities on the basis of gender.
(B) All covered entities shall allow individuals the use of gender-segregated facilities that are consistent with their gender identity. Gender-segregated facilities include, but are not limited to, restrooms, locker rooms, dressing rooms, and dormitories.
So no.