First off, if the campaign you're considering making is supposed to be Player Characters (PC's) being put into a world of two extremes you aren't taking it far enough.
If it's a Thought Experiment:
The Order of the Scarlet Woman will have to allow total homosexuality and use the charm spells on the men as well should they not be interested in sex. They would also be unable to leave.
And since you will have high ranking women in the order they will have to also kidnap men they consider handsome and the order will have to assist. And not merely assist, wholeheartedly agree with her actions.
The Order of the Virgin will have to force men to marry as well since it is realistic to assume there will be those who do not wish to. And not just because they are gay, a player, or dislike sex.
It is also reasonable to assume that women will have discovered ways of manipulating their environment to force certain men to be with certain women, so being beautiful/handsome in your world would have a number of automatic dangers.
Sex and Gender Spells.
Then of course there are the polymorph/curse spells made permanent which would turn wo/men into wo/men and expand the potential targets for either side.
This is more likely to be done by the order of the scarlet woman but it's use by the order of the virgin is almost certainly done as well.
Then again, if you're going to accept the effect of the polymorph/curse spells then why not expand it to hermaphrodites? (Both at once.)
This would probably be limited to the order of the scarlet woman.
If this is not merely a campaign based upon the characters examining the two extremes and is instead based upon your own, personal prejudices...
I'd say you aren't thinking far enough into the future.
Women are automatically physically weaker than men?
A few dozen decades of breeding programs would switch that around.
Especially if the program focus was also on breeding men who'd be physically weaker.
Granted, this ignores the advantages equipment can have in making personal strength irrelevant.
A man a woman both have machine guns and unlimited ammo. Who wins?
But let's make it clearer.
A woman and a man both have tanks with unlimited fuel and ammo. Who wins?
For extra fun lets play with genetic engineering. After all that's the realm of intelligence not strength.
You both have access to all the body altering and enhancement serums you wish. Which one will win?
While you haven't said it explicitly your order of the virgin sees women as the baby makers?
It's only a matter of time before artificial wombs are created and used with artificial insemination so women will be able to avoid the unpleasant aspects of pregnancy. Granted, that will cause them to not experience the pleasures associated with pregnancy and might cause unexpected social problems, but we won't know how bad or even if they will occur until it happens.
And if artificial wombs are created it will only be a short time afterward that implantation of those wombs into men will be proposed for those interested in experiencing pregnancy for themselves.
Granted, this is a near future thing for ourselves and not a concern for those of the medieval age.
Unless you take into account Spells and Artificers...
Outside of futuristic considerations:
A woman wouldn't be able to crush both of these orders on their own through brute force?
Realistically? Probably not, but by the same token a single person couldn't defend either of these orders by themselves through brute force so it's irrelevant.
Considering the stability or likelihood of either Order?
The Order of the Scarlet Woman looks like it has a limited lifespan.
While the Order of the Virgin would be at risk of losing half of it's population potential application to diplomatic, economic, scientific, philosophic, etc issues the Order of the Scarlet Woman would be allowing women who had to hide their personal opinions on kidnapping, forced sexual activities, and most importantly forced application of charm spells in positions of high authority.
Unless high ranking members, especially high ranking female members were to automatically be placed under charm spells the order would quickly tame itself, if not tear itself apart entirely.
Even if high ranking members were automatically put under charm spells it would only slow the orders rate of collapse.
Lower ranking members who hid their personal opinions would be looking for ways out of the order and if they found one would take it. Probably pulling other members along with them.
If all members of the order have charm spells placed upon them the problem still isn't halted because if the orders use of mentally affecting charm spells is public knowledge (And it would become public knowledge via the criminal underground.) then the public would consider joining or being dragged to the orders headquarters tantamount to "personality death."
On the Battlefield.
This is without the natural advantage opposing forces would have against members of the order of the scarlet woman when using dispel or greater dispel against the orders troops.
Someone who is suddenly free of the compulsion to agree with the orders dogma is going to less likely to be effective in combat and much more likely to be teeth-grindingly upset about what was done to them.
Tactically, if I wanted to take out both oders it seems like the order of the virgin would be the one I'd destroy first. The order of the scarlet woman would either hemorrhage it's populace and members to my side if they aren't automatically charming everyone, collapse, or be so weakened by the loss of their main enemy that they could be taken relatively easily.
Politically however, to get the numbers needed to take on either side would probably require fighting against the order of the scarlet woman first since a merely repressive society would beat out a society which practices personality death, followed by physical and psychological abuse.
These options however are based on the idea that these are the only two options available to those looking for truly powerful backers during a takeover bid.
Which seems unlikely.
Personally,
It is interesting that of the two extremes it is the order of the scarlet woman who have decided that charm spells are required.
It gives the appearance of weakness to their cause.
The problem your orders and potentially you too have from your use of "Miss" instead of "Elf Witch" is the application of what I believe is called the Golden Rule.
"Do unto others as you would have done unto you."
Translation: "Treat others in the same way you would like to be treated."
Personal Translation: "If there is something you wouldn't want to have happen to you, then don't do it to other people."
I think that's from one of the Adam and Eve based bibles, but I'm not sure.
