Conchita Wurst is the stage persona of Thomas Neuwith - a gay singer. He is male, identifies as male. Dresses as Conchita Wurst to perform in drag (the clue's in the somewhat humorous name name wurst=sausage)
Thomas has been absolutely clear, repeatedly, that he is a gay man who works as a drag queen and has no intent to transition. I am not at all impressed with people trying to appropriate his hard work. As the character of Conchita (for whom "she" pronouns are used), she has an absolutely cracking voice.
By contrast Dana International is fully transitioned. I don't see why people can't handle both these realities.