how to cluster inseparable data
As you point out, the problem is not on the clustering algorithm, but on the features. So the question comes to the particular data you might be dealing with.
As an example, say you want to cluster different kind of animals. It is in general much easier to tell an elephant from a horse apart. But if you want to distinguish between races of horses, it gets much harder. But the bottleneck lies (mostly) on the features.