Not 100% true, unless they are falling in a vacuum. In atmosphere, the amount of air resistance acting on an object in freefall is proportional to the mass, surface area, and velocity of the object. Mass and surface area remain more or less unchanged, but velocity changes as you are subjected to more and more acceleration due to gravity. Eventually, for all objects, there is a point where the air resistance causes the same force as acceleration due to gravity, and you no longer accelerate; this is called Terminal Velocity.
A person falling through the atmosphere has a terminal velocity of about 120mph. But a small dog or cat has a terminal velocity of 50-60mph.
An empty shotgun shell, when dropped without any spinning, will have the brass end fall first because the open end has much more air resistance. Of course, if it stays in freefall, the inertia from it rotating around its center of mass will cause it to continue to rotate, but the difference in air resistance will cause its rotation to be unpredictable.