The court has already ruled, in effect, “We don’t care what the legislators thought in 1964, the text of the law is clear,” said Roy T. Englert, a Washington appellate lawyer who is the lead author of the brief. The issue of nondiscrimination protections for gay and transgender individuals may stir up cultural and political disagreement, but as a matter of law they should be straightforward, Mr. Englert added. “It’s encrusted with a lot of baggage, but it’s actually really simple.”

The brief argues that discrimination on the basis of sexual orientation or gender identity is, at its core, discrimination against someone because of his or her sex and violates Title VII of the Civil Rights Act.

People who are fired because they are gay or lesbian are being treated differently for engaging in behavior that would be tolerated from them if they were members of the opposite sex — in these cases, a man who is attracted to a man or a woman who is attracted to a woman.

It applies the same logic to discrimination against transgender individuals.

Most federal appeals courts have interpreted Title VII to exclude sexual orientation discrimination. But recently courts have split over the question. The cases the Supreme Court agreed to hear include one from New York in which a gay skydiving instructor said he was fired after a female customer complained about being tightly strapped to him during a tandem dive. The instructor, hoping to reassure her, told her that he was “100 percent gay.” Judges from the United States Court of Appeals for the Second Circuit concluded “sexual orientation discrimination is motivated, at least in part, by sex and is thus a subset of sex discrimination.”

In a second case from Georgia, judges from the 11th Circuit reached the opposite conclusion, that sexual orientation-based discrimination and sex discrimination are not the same thing. The third case the Supreme Court will hear involves a woman who was fired from a Michigan funeral home after she announced in 2013 that she was transgender and would start wearing women’s clothing to work. Judges in the Sixth Circuit sided with her, ruling that sex and gender identity cannot be disentangled.

Some conservatives have balked at the suggestion that it would be fundamentally conservative or textualist to see the law as covering sexual orientation and gender identity. The purpose of outlawing sex discrimination, they have pointed out, was to produce gender equality — not to tackle other forms of discrimination.