Many years ago in my early 20s, I was falsely accused of sexual harassment by a coworker. She wanted to go out with me for the longest time ,and when she finally asked, I declined. She asked why, and I said it's because she smokes and I don't. The next day I got brought into HR and was accused of sexual harassment. I explained my position. They said it was her word against mine, so I said if that's the case, then they should be aware that her past 2 boyfriends both have restraining orders against her. One she stabbed, and the other she hit with her car.
they did their investigation, and a week later I was cleared and she suddenly moved out of state. But that was the only time it's ever happened, and i'm in my upper 40s now. So it's not something I worry too much about of happening, and I don't think most men should. If there's any men who have a reason to be genuinely afraid of being falsely accused (not just sexual crimes, but crimes in general), it's black and latino men. That still happens with unfortunate regularity, relatively speaking.
Really though, with how many women are assaulted and harassed and how our society still treats them, they get it much worse than we men, and they should get benefit of the doubt.