Is the C-word really treated as a misogynistic/derogatory slur against women in the US?

I ask because I notice how in the rest of the other English-speaking countries, the C-word is never treated as a misogynistic word since here in the UK, the C-word is applied as an insult to both men and women and women here don't get as easily offended by the word as American women do. The US on the other hand (yes I've traveled to the US once), god-forbid you even mention the C-word near a large group of women (especially if they are progressive-leaning).
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Is the C-word really treated as a misogynistic/derogatory slur against women in the US?
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