How did womens experiences in civil rights and antiwar protests increase their awareness of sexism?
A feeling of equality.
I think they were aware of sexism well before the civil rights movement. For example, during World War II in the United States, women were needed to serve in areas previously occupied by men, because the men were needed to fight the war. After having a taste of this independence, opportunity and their expanded abilities, they were pushed back into their subservient roles. (You may never know that you live in a cage, unless you become aware of what is outside of the cage.)
Since this is not my area of expertise, I searched Google under the key words "sexism history" to get these possible sources:
http://www.edenbridgetown.com/ethics/discrimination/sexism.shtml
http://en.wikipedia.org/wiki/Feminism
http://en.wikipedia.org/wiki/Sexism
http://links.jstor.org/sici?sici=0022-2445%28197108%2933%3A3%3C541%3ASIHOWW%3E2.0.CO%3B2-7&size=LARGE&origin=JSTOR-enlargePage
http://www.rootsofsexism.freeuk.com/
I hope this helps a little more. Thanks for asking.