A League of Their Own is set during WWII, which followed a nadir for feminism during the Great Depression.

Wonder Woman came out as the first feminine superhero in 1941. Eleanor Roosevelt was also a visible figure of feminism, as she functioned as a diplomat and public figure. "Rosie the Riveter" was a series of advertising posters commissioned by the US Government to help recruit women for wartime work.
Many women did factory and other jobs during WWII. There were record numbers of women in the workplace then. My grandmother built ships for the war (a la Rosie the Riveter) and wanted to work in the auto factory after the war, but she was told these jobs were promised to the returning soldiers. She wasn't alone in being told that sort of thing. 3 million women joined unions because factory owners were underpaying women relative to men for the same work-- welding, etc.

Women also took over driving buses, trucks, and jeeps.

Another aspect is that 350,000 women in the US served in the war in auxiliary roles-- nursing, office work, flying planes, training new pilots and men on gunnery, did war equipment repair, and other things to free up men to fight. Some even worked as codebreakers. The Marine Corps Women's Reserve was created in 1942, and 18,000 women had enlisted by the war's end. They were considered Marines and took over key support positions-- driving, instruction, etc. all to free up men to fight overseas.

Even though underpaid, many women found themselves freer and more independent during WWII, while serving patriotically as civilians or in the military. Many of these freedoms were curtailed after the war, when they were expected to return to housewife lives again--leading to social unrest that would culminate in the women's rights movement.
After WWII, women's participation in the workforce dropped to 30-40% of the workforce in the 1950s'. (Lower class women have always had to work.)

To recap: many American women got a taste of camaraderie, confidence they could do a man's job, resentment that they were not appreciated for that fact, and developed leadership skills that would translate later on in unions, and then later on in women's organizations.

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As for how many men were sent off to war, it was a staggering number: 16.35 million Americans, both men and women, served in WWII, out of a population of 140 million. That's 11% of all Americans, drawn mainly from the eligible ages of around 21-45 years old. 2 million fought in Europe alone.
Per the Selective Service Act, potential enlistment ages were 21-44. although men ages 18-65 had to register for the draft. By October 1942 it was decided anybody over 45 was IV-A: overage and unfit to draft. So this is a major exodus of men. Some occupations such as miners, steel factory workers, etc. were exempt from the draft.

They were calling up medical rejects by the end and assigning them to office jobs, anything to free up able-bodied men to fight overseas. Isaac Asimov in his biography talked about serving as an army clerk even though he had been rejected early on as unfit, he was just assigned instead to a supporting position. (He was around 19-25 years old during America's participation in WWII.)

Women were also more often child-free (or with grown children) during WWII and able to serve. You see, people born from 1928 through 1945, end of WWII are called the Silent Generation because they were far fewer than the Baby Boomers (1946-1965). WWI & the Spanish flu epidemic wiped out a lot of young people. Then there was a great depression and then WWII-- all factors that slowed birth rates.

Many of the Silents fought in Korea, as well. They formed the leadership of the Civil Rights movement in the 1960s, and created 1950s-1960s rock music.

President Joe Biden is our first president ever from the Silent Generation: he was born in 1942, during WWII. We've had 4 Baby Boomer presidents in a row. Before that, from 1953 onwards we had an unbroken streak of 8 presidents who served in various capacities in WWII themselves, through George Bush Sr.