The application of the principle is subjective. However, "subjective" does not equate to "preference" the same way aesthetics do.
There are obvious extremes. A class with exactly one method, with only a few lines of code, which does not call out to any other classes, is definitely following the SRP. On the other hand, a class with two methods, one which contains a complete e-mail implementation through raw sockets and another which builds up a GUI form, is definitely not following the SRP.
Aesthetics are a poor analogy. A better analogy would be the well-known computer science concepts of coupling and cohesion. Neither of these are black-and-white, true-or-false attributes. However, they are measurable, even if there's a qualitative element. If you show a group of experienced developers two separate designs for the same feature, they are going to give similar readings on which design has more coupling and/or cohesion.
In fact, the SRP is essentially just functional cohesion. It says that the parts of some module (e.g. class) should be grouped together because they all contribute to performing the same function, and for no other reason. "Function" may be subject to interpretation - some people may interpret this literally as a single function (or method or procedure) declaration, others may step back a bit and think of a function as "sending e-mail" or "playing music", but there is still only so much room to maneuver. "Managing stuff" is not a valid functional description.