The economy that drives burlesque is the trade of price-of-admission for the God-given attractiveness of the female form. This trade is, of course, inherently sexually biased for obvious reasons. One could argue that it's unfair because men can't perform because men don't (usually) have women's forms. Alternatively one could argue that it's unfair because it exploits women for the lowest-common-denominator quality of their physical shapes rather than using anything more elevated such as their talents or intellect. These objections are political. However, in the modern era, burlesque shows have been staged by people (perhaps even feminists) who reject any of the arguments and present their shows with tongue in cheek (which means mischievously, or ironically). Your quote is basically saying that presenting something in an ironic way is guaranteed to deflect any criticism, since criticism can only hold water if the person being criticized is sincere. If they're not sincere--if they cling to the "I was only joking" defense--then they can't be criticized. This is the theory. The term "fairy dust" (which literally means dust sprinkled by a fairy to have some magical effect) implies (to me) that the commentator is recognizing that irony is an at-least-somewhat dishonest tactic in and of itself.

Yikes. That's an awful sentence. You'd really need context to know what exactly it means. "Fairy dust of irony" is not a turn of phrase in English. It might mean "a subtle coating" in the sense that a bit of irony causes burlesque (the style of dance?) to be less politically significant/charged. But again, that's making a big guess on the context.