No, women were exempt because cubicles countries recognize the need for mothers to be with their children. The feminist movement said that’s all bunk - and now we have “conservatives” agreeing with the feminists
They were legally exempt by SCOTUS in Rostker v. Goldberg. SCOTUS decided that women were not required to register:
And since women are excluded from combat service by statute or military policy, men and women are simply not similarly situated for purposes of a draft or registration for a draft, and Congress' decision to authorize the registration of only men therefore does not violate the Due Process Clause.
Since Obamas policy has now put women into combat service, it violates the Due Process Clause.