Why is "would" being used here? Would the nuance of this sentence change if I replace "would" with "didn't"?
Yes there is a nuance. "Didn't" simply past tense, if it were used in this sentence it would mean that men never confused them with higher status women. "Wouldn't" is used because the narrator is taking about the future in the past. Meaning that the decision about red lipstick in ancient Greece was to try and stop any confusion, but unlike "didn't", "wouldn't" is ambiguous and does express if this worked or not. Ex: I skipped breakfast so that I wouldn't miss the bus. (We still don't know if they missed the bus or not) Ex: I skipped breakfast so that I didn't miss the bus. (We know that they caught the bus) Please note that while this is the rule, you will notice in casual conversation between native speakers that they do not always follow this rule. They will sometimes use the two words interchangeably.
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