Telling someone to "be kind" is not intrinsically gendered, obviously, Using it as a tone-policing and silencing tool is usually done to women, and therefore becomes gendered behaviour in those situations. You'd probably have to be a women experiencing this to really get it.

And to clarify - trying to "be kind" is a good thing. I believe we should start by assuming the best of someone instead of the worst. It's when the phrase is used disingenuously that it's a problem.