In Chapter 27 Emma, always so quick to see the faults in the manners of others, does not come over as behaving quite like the perfect lady herself. Lets take her remarks on the Cox sisters, whose brother Emma dismissed back in Chapter 16 as a possible husband for Harriet, though only in soliloquy, with "Oh! no, I could not endure William Cox -- a pert young lawyer." (How Harriet could endure young Mr Cox is clearly irrelevant). First she tells Harriet that she thought the Cox girls, fellow-guests at the Coles on the night before, looked "Just as they always do -- very vulgar."
I'm sure the conduct books of the time would not rate that as a very genteel observation.
Harriet then mentions that Robert Martin dined with the Cox family on the previous Saturday, that the Cox girls talked a great deal about him, especially Anne Cox, of whom Harriet says "I do not know what she meant, but she asked me if I thought I should go and stay there again next summer." And Emma says "She meant to be impertinently curious, just as such an Anne Cox should be."
So it's all right for Emma to try to elicit Jane Fairfax's personal opinion of Mr and Mrs Dixon's prospect of happiness in marriage, but it's not all right for Anne Cox to ask a somewhat less intrusive question. I am reasonably sure that Emma regards herself as a perfect lady (except on these redeeming occasions when her own heart tells her she is not behaving well) and she certainly regards the Coxes as "Without exception, the most vulgar girls in Highbury." Yet both Emma and Anne were trying to get information about something of interest to them, and of the two of them Anne's motive - an interest in an eligible young man - is rather less discreditable than Emma's, to try to get evidence that her Jane Fairfax/Mr Dixon fantasy is true.