Is it wise for a man to be cautious around women?

Nowadays we live in a society where if you look at a woman the wrong way, you'd be accused of sexual harrassment or called a creeper. Personally, I'd never disrespect a woman. However, seeing that some guys harrass women, I could be folded in the mold as a harrasser because one guy did it. It's gotten to a point that if a woman sat next to me, I wouldn't acknowledge her at all even if she said hi. I know this sounds rude, but at the end of the day, no woman is worth me losing my freedom. It sounds paranoid, but I have think about myself. Wise or not?
Is it wise for a man to be cautious around women?
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