You can't calculate entropy without defining the macroscopic variables you are interested in.

Once you have done that, you can start counting the microstates that satisfy those macroscopic variables.

So, in other words, yes, entropy is subjective, and depends upon your definition of variables (and ordering). What's the other argument, leading to debate?

    ΔS = Q/T

We tend to think of energy as an objective thing (the distance your car can go on a tank full of gas doesn't depend on your subjective beliefs), and the same is true for temperature (commonly manifesting as an average energy and measurable via thermometers). This implies that entropy should be considered an objective property of the system as well.

So then, would this be true:

The specific value for the entropy of a system depends upon the definition of the microvariables. However, regardless of the definition used, the measured value will increase over time. In the deck of cards example, above, one definition of entropy is the suites and rank, and another definition is the numbers 1 .. 52 written on the backs. Shuffling the deck will reduce the ordering, no matter which definition you look at.

This implies

a) No definition of microvariables and their ordering can result in an entropy level which is the inverse of another definition.

b) Its possible to define a set of all sets, which is the union of all possible microvariables and orderings. This uber-entropy will also increase over time.

I suppose the philosophical argument is that "objective entropy" is either referring to the uber-entropy, or the property that all entropies always increase, and "subjective entropy" is looking at specific values for one particular measurement system.

Also, c) increasing entropy over time only holds true for interaction functions which are fully transposable. For example, if microstate X is the result of an interaction "f" betweeen microstates A and B

state(x) = f(state(a), state(b))

state(a) = f'(state(x), state(b))

state(b) = f''(state(x), state(a))

f, f', and f'' are fully deterministic and yield unique results for every combination of inputs.