I think you missed the point. Throughout the feminist movement for equal rights, we just never seemed to hear any demands that women also have equal responsibilities in the USA.
And it’s not a question of whether one believes a draft system should exist. It does exist and if women want equal rights, they should also want equal responsibilities. And there would obviously be some draft deferments for women not available to men.
The feminists avoided that issue because they knew what a volatile issue it would be and supporting that equal responsibility would have turned many against their overall cause.
That goes right in line with a point that Dr. Jordan Peterson has made many times. He says it’s very telling that modern feminists argue “equality” when they talk about a lack of women in government leadership and corporate executive positions, but they never complain that there aren’t enough female bricklayers or prison inmates.
feminists never said they wanted to pick up the check
“we just never seemed to hear any demands that women also have equal responsibilities”
Responsibilities exist without compulsion by others.
The responsibility exists, and plenty of opportunity exists to serve.
Responsibility is obligated only when inadequate numbers volunteer.