WASHINGTON—The Supreme Court will hear three cases concerning whether gay and transgender people are protected from discrimination on the job, marking the first major LGBT rights issue to reach the court since its 2015 opinion legalizing same-sex marriage.

Lower courts have differed sharply on whether the 1964 Civil Rights Act, which prohibits sex discrimination, necessarily covers sexual orientation or gender identity. Congress, unlike some two dozen states, hasn’t explicitly added those classifications to federal antidiscrimination...