Yeah, I understand how acceleration due to gravity is independent of the mass in question. My problem comes in with the any other force part. All of the examples you cited (A spaceship and a black hole. A baseball and the earth. Chris Squire and Spandex) are just more gravitational interactions, unless I misunderstand you.
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The acceleration two objects experience by the same force is independant of the mass of those objects.
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If I construct a device to strike a bowling ball and a feather with the same force (in a vacuum and assuming the feather is as rigid as the bowling ball and won't absorb most of the force), the acceleration imparted to the feather will be far greater due to its lesser mass. Gravitational acceleration is independent of the mass, because it is always the force that changes due to the mass and acceleration, not the other way around (so you always have
different forces acting on the objects). However, given the
same force to impart an acceleration, the mass will most definitely affect the outcome.