With Haidée, Byron basically wants to point out not just the double standards of what was supposed to be a rigid society with specific gender roles, but also the complex nature of romance in general.
Haidée, as a product of her time and place, is expected to fulfill the damsel role. She is particularly expected to do so since she has had the most exemplary upbringing by the Greek Orthodox Church. This means that she should be an example of virtuosity and, at the same time, that she has become well-groomed to become the epitome of a well-bred and dignified future wife.
However, Byron dashes a couple of shades of salacity upon Haidée as well. We know that she is quite sensuous, idealistic, and prone to fits of passion. Her heart rules over everything else and there is a clear indication that sex is a weakness for her whether mentally or physically. Yet, Byron describes her as a pious woman, and that contrasts dramatically with what her actions clearly expose.
Also, keep in mind that Don Juan is in itself satrical to begin with. The characters are meant to be paradoxical and their situations are meant to bring on comic irony.
Back to Haideé, after learning more about her character we come to realize that while she continues to be thought of in one way, her behaviors leave much to be expected. Remember that, after all, she was ready to jump on Juan when she first sees him lying almost dead by the island shore and she was, literally, taken over by sexual passion. In canto II she wanted
"to take him in,
A stranger" dying-with so white a skin. (Canto II, St. 129)
Also far from a damsel in distress, Haideé is strong, and possesses more "male" characteristics than Juan himself. Juxtaposed to him, she is stronger, more invasive, and almost the embodiment of what a "Don Juan" is meant to be.
Clearly all this ironic characterization is aimed to produce satire, and it makes the reading lighter and much more in-depth than by characterizing Haidée as yet another weakling female character.