I think you're quite right about applying Modern concepts. Emma IS first lady in Highbury and yes she does regard herslf as an arbiter on social matters, that's what women of her class did.. THey were regarded as the organisers and judges in the field of "society" as social interaction... rahter than men. So she's quite "normal" in that respect for a woman in her class and time. SHe's not cosying up to people of a higher clas than her, and admiring thtem because they are socially superior, as Sir Walter ELliot does.

She is quite right ot regard the Martins as "not her class". They are not her class and Mr Knightly does not invite tehm to dinner or parties. Compared with most of hte gentry they are consdiered vulgar and coarse. Most gentry folk would say they were fine people, hard working intellignet and sure to do well with teh farm but that did nto mean they had the social graces or hte tastes of gentlefolk. They were in their sphere and Emma and Mr K are in their sphere and while Mr Knightly as a landlord may mix with them, there's no need for Emma to do so....
and as you say words like "illiterate" have chagned meaning.. it does not mean that he can't read but that he's relatively uneducated, does not read much or for pleasure.