If an object is hinged, then it is obvious that we should be calculating moments about the hinge, since the object is only capable of rotating about the hinge.
If an object is unhinged, it’s motion can always be analyzed as the superposition of the rotational motion about its CM (centre of mass), and the translational motion of its CM. Since the rotation is about the CM, we should calculate moments about the CM!
As an example, let’s consider a ball of radius 2 m subjected to forces applied at different points of the ball. Can you deduce whether the ball is in rotational or translational equilibrium for the following scenarios?