Emma may be snobbish to the Coles, or intend to be but gets sidetracked by her desire for a good party. But the Coles are just as snobbish. They invite the male Coxes to dine, but the "less worthy" female members of the family are only invited for the evening. The same is true of Miss Bates, Miss Smith and Miss Fairfax. The Coles think they are worthy of dining with the best families, but they find the unmarried, unrich lady's of Highbury to not be worthy of dining with them. Emma intends only to show the Coles the same sense of superiority that the Coles show to the Misses Cox, Fairfax, Smith and Bates. The Coles certainly do want to see the delicacies of rank preserved, when it is their rank being preserved.
It is rather a parallel with Mr. Elton. Mr. Elton is well aware of the fact that Miss Smith is beneath him. But he doesn't see that in situation and fortune he is quite beneath Miss Woodhouse.