This isn't quite correct, in the present state of affairs. Young men have to register with selective service, and stay registered from age 18 to 25, but young women don't. If we needed suddenly to call people up, I think it would be our young men. In such a crisis, you're not then going to suddenly have women register too.
This prompts a question that had never occurred to me. Now that we've become so egalitarian about women serving in the military, why haven't we extended that requirement for selective service registration to women as well?
(And why hasn't it come up in any of CFC:OT's MRA-driven debates about institutionalized sexism disfavorable to men?)
I regard myself as just having lucked out of military service, by our not having a war that required a draft for the seven years I was on tap. So I'm not sure I'm any better than any of the people on the OP's list who "dodged" military service, whatever that means in each of their cases. I thought about getting conscientious objector status, but never bothered to pull together the file.
(When Army recruiters called during my senior year of high school, I told them I was going to college. When they asked me what I was going to study, I told them "peace studies." Ended the calls real quick. It wasn't entirely a lie, though in the end, I didn't major in peace studies; I looked into it, but it was a very disorganized program at my college. But I was pretty pacifistic back then, so I think I could legitimately have substantiated C.O status.)