The key element that causes Daisy Miller to be shunned by respectable society in this excellent novella is the low social class she occupies. Note how in Chapter Two, Mrs. Costello points towards this by giving a number of reasons why Daisy Miller and her family should be shunned and not accepted into polite society:
"They are very common," Mrs. Costello declared. "They are the sort of Americans that one does one's duty by not--not accepting."
If this were not censure enough, Mrs. Costello later backs this up by saying:
"She is a young lady," said Mrs. Costello, "who has an intimacy with her mamma's courier."
So, in spite of the way that Dasiy Miller dresses incredibly well and is very fashionable, her low social status and the way that she and her family mingle with servants and people who normally have nothing to do with their betters points towards why, in the eyes of Mrs. Costello and others, they must be shunned.