I'd like to inset a face that would-be created by being reflected across the x axis.
When I try to inset this face, Blender tries to inset only the half of the face on the editor side, rather than creating a new inset of the whole rectangle that includes the other half as well.
How do I adjust this?
If I understand you correctly, then after I for inset hit B for boundary. That tells Blender whether to consider the open edge when insetting or not.