Typically input is male, output female. Its a safety thing. The female output ensures you don't get zapped if the output somehow was floating high above ground and you touched the prongs.
Not what I've ever owned or seen. All my XLR chassis mounts are male at the source end (Modwright Transporter, Preamp outputs, processor outputs) and female at the receiving end (preamp inputs, amp inputs). IMO, your comment is only true for cables, not the OP's question (chassis mounts, i.e the opposite of cables).