My browser's spellcheck says it is, but I can't figure out why. Is Firefox sexist?
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No. It is not (necessarily) a typo. The following examples are all perfectly acceptable uses (at least grammatically) of the possessive form of women.
I am unable to answer your question about whether or not Firefox is sexist.
"Women's" is the plural possessive. If you're referring to one woman you should say "(a) woman's" instead.