Am I being unreasonable?

I hope you are keeping a log.

This is the same staff member who, in *their* performance review, told me that my boundaries are too strict and that it upsets them that I'm not their friend!

Oh gosh. That's... wow.

What's the culture like at your job? Are women expected to be touchy-feely and BFFs forever and be punished for being "cold and ruthless" (ie doing their jobs the same way any bog-standard man would) if they push back on that?

Because the response to that would have to be something like, "Mary Sue, this is at heart a professional relationship. If you have concerns or difficulties with your work, or difficulty in your private life which may impact your work, please feel very free to come and talk with me about it so that the company can help, but this is by nature a manager-team member relationship and needs to remain so," but of course women get in trouble for saying that sort of (very necessary) thing.

I hope you are keeping a log.

I second this. Just email yourself and file it every time. People like this turn into big problems in my experience and you don’t want to be starting from a blank slate when that (inevitably) happens. And if it never happens, no harm done.