[Filligree]

> Is there a non-gendered equivalent to man-up?

Yes, it's "man-up". "Man" is, like it or not, a reference to the species there.

[maxerickson]

In that context it is literally a reference to traditional male behavior (that could be expanded as expected male behavior in response to adversity).

[nilved]

? no it isn't, and even if it was that would still be sexist