It is physically accelerating it's not just mathematics, the ground is constantly exerting an upwards acceleration against free-fall. Actually it's pretty cool you can check this out for yourself : download an accelerometer app on your phone. Let your phone stand still on the ground, it will measure an upward acceleration of 9,8 m/s². And if you drop your phone, during the drop it will measure 0 acceleration. This is actually not just a subtelty, discovering that it's the ground that accelerates upwards is what Einstein called the greatest idea of his life. It's the core idea of general relativity, allowing us to understand gravity. Gravity is exactly the same kind of force as the one that "pushes" you back in a car when you accelerate.
For a parachute, the ground is pushing the air which is pushing the parachute. This is also true for the surface of the moon, but more generally any solid object. The electrons in the atoms that make up solid objects generate repulsive electromagnetic forces, cohesion forces. These forces are the reason why such objects are solid, if you try to compress a rock for example it's hard, because its atoms are exerting an outward force to prevent the rock from changing shape. On the contrary if you think of a cloud of gas in outer space, it does not have such cohesion forces, therefore the cloud does not exert any outwards acceleration. The gas cloud contracts along with the grid, which is how stars are formed.
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