Yes... women should ALSO be required to register with the Selective Service.
Practically speaking, females would be relegated to support roles by default given their stereotypical physical attributes...
Which frees more men for actual combat duty, just as we saw in the 1940s...
Although, nowadays, any female desiring to join the combat arms should be given a fair chance to train and participate...
We hear a great deal of talk presently about various service branches struggling (or even failing) to meet recruiting quotas...
Perhaps it's time to dust-off the long-dormant Selective Service system and to conduct a limited draft to compensate...
The Draft might also be used to top-off any staffing deficits in Reserve and Guard units if-and-as needed...
Resurrecting the Draft would also help to "re-balance the load" for national defense so that it's not just The Poor enlisting...