According to Wikipedia, these are the contentious passages of that proposed U.S. ENDA law:
Section 3 (a) (6) GENDER IDENTITY- The term `gender identity' means the gender-related identity, appearance, or mannerisms or other gender-related characteristics of an individual, with or without regard to the individual's designated sex at birth.
Section 8(a)(3) CERTAIN SHARED FACILITIES- Nothing in this Act shall be construed to establish an unlawful employment practice based on actual or perceived gender identity due to the denial of access to shared shower or dressing facilities in which being seen fully unclothed is unavoidable, provided that the employer provides reasonable access to adequate facilities that are not inconsistent with the employee's gender identity as established with the employer at the time of employment or upon notification to the employer that the employee has undergone or is undergoing gender transition, whichever is later.
Section 8(a)(4) DRESS AND GROOMING STANDARDS- Nothing in this Act shall prohibit an employer from requiring an employee, during the employee's hours at work, to adhere to reasonable dress or grooming standards not prohibited by other provisions of Federal, State, or local law, provided that the employer permits any employee who has undergone gender transition prior to the time of employment, and any employee who has notified the employer that the employee has undergone or is undergoing gender transition after the time of employment, to adhere to the same dress or grooming standards for the gender to which the employee has transitioned or is transitioning.
So far as I can see, all it says is that employers have to let people have the same freedom to dress as the same gender they [simplified] do at all other times, and that they are permitted to segregate trans people from other people in change rooms and showers provided they let them use some other facility. This is awful enough to need cutting from a law before prohibiting people from discriminating in the workplace over who sleeps with who outside it?