Maybe instead of insiderhood, you should consider it merely as a signal of non-ignorance,

I quoted the first sentence from wikipedia. That is the definition of classical music that matches what most people - most certainly including Nancy - mean when they say 'classical music'.

specifically of the fact that "classical" is the name of a historical era.

I am well aware of the historical era. Declaring that by relaying the common usage definition of 'classical music' I must be ignorant of the classical era is itself a strong signal of being unaware of how human language works.

One group in which I like to signal myself an insider is 'Science'. We still use the word atom for something that can be broken down into protons, neutrons and electrons - and even the latter is a simplification. The relevance should be obvious.