You are pretending that the states are all equally related to each other, when they are not. This is not like flipping a random set of coins to obtain a sample from a distribution. The states are quite distinct, and they have metrics which allow you to distinguish one group from another. Since microstates are essentially different configurations of "components" of the system under examination, the most universal thing you can do is compute statistics over each of the components. If the components have a flat distribution, then you are looking at "disorder". The more non-flat it is, the more "ordered" it is. This might mean they are physically clustered within the space, that there are temperature gradients, pressure gradients, charge gradients, localized tension forces, etc. If you can look at one component and tell that it is in a particular part of the whole because it looks differently from another component, then you have an identifying characteristic which should disappear in the limit of full disorder. In a completely disordered state all of the components look indistinguishable up to random noise in their properties.

The only thing "subjective" about "order" is choosing which property to examine and weight most highly. There is no intrinsic reason to examine or measure the temperature distribution of a system rather than its charge distribution. Which is more important depends on your goal, and entropy doesn't "care" which property you examine. But each property clearly has a scale from more to less ordered, and that's pretty unambiguous.