Men are able to serve in any military occupational specialty in our armed forces if they meet predetermined, nongender specific, prerequisites.
While women have traditionally been barred from front line combat unit service (i.e. Infantry, armor, artillery, special operations, and others) specifically due to their gender, the Secretary of Defense in Dec 2015 announced that those occupational exceptions would be lifted.
All American men age 18 to 25 are required to register for the selective service.
If women are now allowed to serve in all military occupational specialties without limit, then they should also be subject to the same civic requirements as men.
Therefore all age appropriate women should be required to register for the selective service as well.