I suppose if we include dynamic response, and drop the rigid body assumption (allow the cheeses to compress), then in an infinitely long set of cheeses, the "last" cheese would never feel the force applied to the first cheese. This, however, is primarily because in an infinitely long set of cheeses, the last cheese is infinitely far away and the force would simply never get to it. Additionally the mass of the system would be infinite, and what we think of as the inertia of the mass would provide the reaction force keeping the entire system in equilibrium even though there is no real reaction at the other "end" of the stack. What is more interesting, to me, is that in this same scenario, putting a small force on the "stack" of cheeses would squish the entire stack an infinite amount. I once pointed out in a class that I could make a beam of steel stretch more than 1 foot with my bare hands. Of course, the beam would have to be something like 2,000 miles long...but still, I'm like superman!
In a more realistic case, though, with less than an infinite number of cheeses, each individual cheese (in a horizontal press) needs to experience the same force on the front (top) of the cheese as it does on the back (bottom) of the cheese or it would be accelerating. I suppose that since the cheeses are compressing, the center of mass of the cheese-system is in fact moving away from the piston and towards the "base". Since this is true, and since the speed with which it is moving is not constant, it must be accelerating (technically, not necessarily going faster), which means the net force on the system must be non-zero. If the net force on the system is non-zero, then the net force on each individual cheese is also non-zero. Those cheeses near the piston are accelerating more than those near the base (think of the distance they each travel). Therefore, the cheeses are experiencing different forces and thus different pressures.
Once the cheeses stop compressing, the center of mass is no longer moving, and the net force across the entire system and within each cheese is zero, so they are all experiencing the same force and thus the same pressure. I guess, then, that everyone is right, depending on what part of the cheese pressing they were considering. Some might argued that cheeses are always compressing while in the press--I don't know if that's true, but I doubt it. It seems to me that they get to a point where they no longer compress under a given load.
And now you can agree with my students that I talk too much...and give details they don't really want: "Just teach us what we need to know for the test."