Yes, I agree there is always the possibility of people making false accusations about you to harm your reputation. But they could do that with male to male as well.
I know a female university professor who will not meet with any student, male or female, alone in her office or anywhere behind closed doors for just that reason. She will only meet with a student in a public place like the library.
But Pence appears to be saying that he won’t meet in public alone with a female. I wonder if he would meet with a female alone in private under the circumstances I outlined.
I won’t close my door if I’m in my office with a woman; I know “the game”, and I ain’t playing...