“It imposes selective burdens on men, reinforces the notion that women are not full and equal citizens, and perpetuates stereotypes about men’s and women’s capabilities,” lawyers with the A.C.L.U. wrote in a petition on behalf of two men who were required to register and the National Coalition for Men…

Ria Tabacco Mar, who holds the position at the A.C.L.U. that Justice Ginsburg once had, said the Frontiero decision was proof that sex discrimination by the government without good reason should be unlawful in any part of society. Treating the military differently, she said, “would be a huge disservice to Justice Ginsburg’s legacy and the jurisprudence she created.”

But the challengers must reckon with another precedent. In 1981, in Rostker v. Goldberg, the Supreme Court rejected a sex-discrimination challenge to the registration requirement, reasoning that it was justified because women could not at that time serve in combat.