As others have more eloquently pointed out, a drag act is acting. Whether or not [the person behind Conchita, I forget the name] wants to refer to themselves as 'he' or 'she' is neither here nor there, though it is part of their identity and up to them. When Conchita is on stage, she is a character. A female character. For example, Ms Fritton in St. Trinians. Now, we all know that Rupert Everett plays that character, very much a cisgendered man. However, when we are talking about the character Ms Fritton, and what she gets up to, describing her, we use the pronoun 'her' or 'she', because thanks to the suspension of disbelief expected when watching a film/ show, we know we can use seperate terms.
In much the same way we refer to Drag Queens as 'she'.
As for further trans/ genderqueer issues of pronouns, how about just accept you're cisgendered and don't have to put up with these problems or feelings, and pay trans+ people the respect they deserve, he, she or otherwise.