Women and tribal societies
Women have not fared well in most tribal societies. While some developed into more egalitarian cultures and some even became matriarchies,(Minoan, Sumerian, Hopi, Iroquois, Navajo) the vast majority were lead by councils of men. Times have changed and with it adaptations to grant more sharing of power to people who had previously been very disadvantaged. We've got a long way to go, I know, for I want everyone to have access to learning and economic status and self-determination.
Realistically, the better prepared you are with the mantra of skills, supplies, and seed... the easier any disaster is going to be to deal with. A disaster usually implies victims and rescuers, but it could be a very lonnnnnnnnnnnnng time until that happens. You could starve to death in the interim. Worse, you could be attacked by someone else deciding that you appear weak and helpless and abundantly supplied (even if none of those things).
All skills require learning and some measure of physical strength. I doubt anyone reading this is the world's strongest man or woman, and that's not what we're aiming for. We're aiming for a reasonable level of physical stamina and upper body weight-bearing strength. Most people have quite a bit of untapped strength in their legs, but these need to be trained too with running, especially carrying a pack.
While some women can be more agile in their youth than men, and some can actually be stronger pound for pound than the guys in their lives, that fades as they get older. There's little societal pressure for women to excel as athletes other than a small core of them.
Everyone though needs force multipliers for protection and to help them extend their range of hunting. If you don't possess a firearm, ammunition, and get training, then are you going to rely upon someone else to protect you? That seems counter-intuitive for someone who want self-determination.
We need each other. Both genders possess abilities because of their brains and experiences. People will be good at separate things, and I won't bore you with some ridiculous sexist notion that women are nurturing, because many are NOT. They may make the best shaman sometimes or NOT. They may be the best crackshot in the group or NOT. Let's not be simplistic.
Clearly the preponderance of men at most ages above nine are physically stronger and this has dominated history. In a collapse, a great deal of civility will go out the window unless it's carefully cultivated by leadership and the followers of a tribe. Unless you want to become a second class citizen, then I'd recommend prepping.
It's true that women fell on hard times on the frontier and prostituted themselves. I don't want to ever hear that happening again in any disaster in any period of world history. The majority of women who became prostitutes did so as teenagers because of financial insecurity. Drug abuse most often is the only way to numb themselves and created perpetual slaves. STDs and babies follow and they're stuck in their situations and almost powerless.
What you should also note is that women became tough as nails from working their butts off doing every chore on the frontier, and this is a primary reason that women got the vote so easily in the West. It can go either way in a collapse. It really depends upon your investment in pulling yourself up by your bootstraps (even if you tug so hard they break), develop backbone, and decide it's a priority to better control your life.
Prepping is by its very nature about creating a destiny by your own design (free will), and most likely by working with the Source (submission to Authority). People will define that in different ways.
For Christian prepper women, they may follow Ephesians 5:22 and non-Christian women may get in an uproar. Supposedly the Christian prepper men will also love their wives like Christ loved the Church, which is a much more tougher role and far more demanding. The Christian women preppers I know don't take any guff and are strong and powerful. And this combination with all the other wonderful qualities of women make them fine people indeed.
Regardless of all of that, prep on your own, and don't just half-ass it. Forge that iron in your mettle into steel that is a sharp and strong tool that is also dangerous to mess with.