A heterosexual woman will try to convince a federal appeals court that she can sue her former employer for sexual orientation discrimination, adding a new element to the already-simmering legal debate over LGBT rights in the workplace.

Bonnie O’Daniel, who alleges that she was fired for her Facebook post that disagreed with male-to-female transgender people using women’s bathrooms, said federal civil rights law should cover sexual orientation. O’Daniel will face off against Industrial Service Solutions Inc. during oral argument at the U.S. Court of Appeals for the Fifth Circuit in New Orleans today.

The case comes a day after the...