Assuming that magic use and similar things are not present in the setting, what scenario(s) would lead to female warriors being considered fairly acceptable? The only example that I can think of from real life is Onna-bugeisha from Japan, and I'm clueless on what caused the start of that tradition, though I think one Onna-bugeisha's feats helped make it more popular if Wikipedia is to be believed. Besides such a figure, what could allow female warriors to gain greater acceptance?
The bugeisha (warrior lady) was typically the of a high caste warrior family. The tradition predates the establishment of a formal samaurai class, but persisted until at least the late 19th century.
In a time when men were frequently killed in battle or other dangerous occupations, or simply absent for prolonged periods of time to provide for their families (fishermen, hunters), it fell to the women to take up arms and defend the villages.
The upper classes were expected to lead and participate in battle, and to participate actively in law enforcement. The absence of a man did not alleviate the high class family's duty to lead and defend.
Japanese culture was, by our standards, very brutal. For example, in training a child in swordsmanship, at about 12 years of age they would be taken to the prison to practice getting the right angle to make a good cut on a human body.
It was in this environment that the high class lady was expected to hold her own and prevail over criminals, and to lead militias and armies. Needless to say, with the difference in sheer strength between men and women, their training was less compromising than that of their male counterparts.
Edit: Bugeisha in popular entertainment
The anime "Yona of the Dawn" presents the Japanese cultural mythos of the bugeisha in a popular entertainment. It's the classical story of a spoiled teenage noblewoman caught up in palace intrigue, who escapes and then returns for revenge/justice. While there may have been women who fit this mythos, most of the biographies I have read of bugeisha's indicated that they we nobility that began harsh training at an early age with the intent that they would fight in and/or lead military/police actions.
One possibility would be a awareness. Like in a modern-day society, medieval brutes finally realise that women are human too, liberte, egalite, fratanite, hundred years later: voila, women in the army. I'd like to highlight another one.
No-one else is left
There is an old grim saying. "When are 16-year-old drafted to army? When there are no 17-year-old left anymore."
Female warriors in larger quantities would arise if almost all males (the usual army material) are already killed off. This does not need to be global or even permanent.
To give an example, if all men leave from a castle (unwise, I know), gentry ladies might take weapons into their hands. (A few ifs: it should be Ok to do so, and not only play a damsel in distress, as there are men left, but of lower caste.)
To give a more striking example: Imagine a village in 30 years' war. All men are in army of the landlord. Marodeurs rampage around. Human life is very cheap. Women would bundle-up into some kind of an all-female squad, even armed with improvised weapons, in order to protect themselves.
A corollary is that next generations get a gap. The so-called "demographical echo of the war" would be even more severe in the purposed case. So either some fantasy-level uterine replicators come to the rescue, or the demography drops. The historical remedy from the 30 years' war was to temporarily allow polygamy. It might even not help.
But lo and behold! The effect can be local. So, the one side looses the war, even despite women at war. There should be winners, the now-conquered province struggles to increase its population.
Should such an effort be indeed global (and in absence of artificial childbirth cycle), it spells bad for human race, similarly as an all-in war where almost all males are killed.
There was an historic 20th century effort, but not that large-scale, and it's definitely not medieval.
A seminal event, with a heroine saving the day, might establish a tradition, or at least a respectable choice for female soldiers. An example from Canadian history is Marie-Madeleine Jarret de Verchères, who at age 15 took command of the family fortified manor house against one of the many Iroquois attacks against the colony of New France. The attack took the garrison by surprise and she was almost captured herself. Under her leadership the fort held out for eight days until reinforcements arrived. She was widely hailed as a heroine at the time and since. New France was at that time an embattled colony, where everyone might be exposed to attack by a persistent enemy. Madeleine de Verchères - A Heroine of New France has a readable account and links to further sources.