The US Supreme Court in June of 2021 declined to hear a legal case challenging the male-only draft on the grounds that it was unconstitutional sex discrimination. In the opinion denying certification (written by Justice Sotomayor and joined by Justices Breyer and Kavanaugh) the following is stated (edited for easier readability):

In 2016, Congress created the National Commission on Military, National, and Public Service (NCMNPS) and tasked it with studying whether Selective Service registration should be conducted “regardless of sex.”

. . .

On March 25, 2020, the Commission released its final report, in which it recommended “eliminat[ing] male-only registration.” Among other things, the Commission found that “[m]ale-only registration sends a message to women not only that they are not vital to the defense of the country but also that they are not expected to participate in defending it.” Just a few months ago, the Senate Armed Services Committee held a hearing on the report, where Chairman Jack Reed expressed his “hope” that a gender-neutral registration requirement will be “incorporated into the next national defense bill.”

. . .

It remains to be seen, of course, whether Congress will end gender-based registration under the Military Selective Service Act. But at least for now, the Court’s longstanding deference to Congress on matters of national defense and military affairs cautions against granting review while Congress actively weighs the issue. I agree with the Court’s decision to deny the petition for a writ of certiorari.

A provision requiring women to register appeared in both the 2021 and 2022 versions of the Senate Armed Services Committee's proposed National Defense Authorization Acts, but was ultimately removed each year.