Protections for lesbian, gay, and bisexual workers under current federal law took a further leap toward Supreme Court review after a federal appeals court in New York ruled that discrimination toward a gay skydiving instructor because of his sexual orientation alone could constitute sex bias.

But when the justices might weigh in on a legal question that has for years divided courts and legislatures—and even recently split the U.S government—is still up in the air, advocates on both sides of...